
Class 

Book 

Copyright If. 



COFYRiGHT DEPOSIT. 



LABORATORY EXERCISES 



TO ACCOMPANY 



CARHART AND CHUTE'S 
FIRST PRINCIPLES OF PHYSICS 



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fan 



RAYMOND B^BROWNLEE 

AND 

ROBERT W.^FULLER 



STUYVESANT HIGH SCHOOL, NEW YORK CITY 



>:*« 



Boston 
ALLYN and BACON 

I 9 I 2 



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W 



6 



COPYRIGHT, 1912, BY 
RAYMOND B. BROWNLEE 
AND ROBERT W. FULLER 



/ 

CU328516 



INTRODUCTORY 

SUGGESTIONS TO THE INSTRUCTOR 

Selection of Experiments 

Scope of the Experiments. — The experiments in this book 
provide a wide range of laboratory work for an elementary 
course in Physics. The exercises have been selected on the 
basis of their educational value to the student. Their aim is 
to impart to him certain fundamental principles, to acquaint 
him with some physical phenomena qualitative in character, 
and to show the operation and the use of practical devices or 
instruments that are applications of physical principles. 

The authors have not hesitated to omit from their list 
certain well-known experiments which have persisted in many 
elementary courses, rather by inertia than because of any 
special interest or value to the beginner. On the other hand, 
it is impossible to include in a small book all the experiments 
of merit suitable to a first course in Physics. Yet, from 
those given, it will be possible for any instructor to make a 
selection of the experiments which the great majority of 
Physics teachers include in their courses, so as to afford a 
well-balanced laboratory training, both interesting and instruc- 
tive to the student. 

Recommended Lists. — Only the institutions most favored as 
to laboratory time will be able to complete in one scholastic 
year all the experiments outlined in this book. Any choice 
of experiments must depend upon the apparatus available and 
upon the laboratory conditions. To fit the usual laboratory 
equipment and to meet the time limitations of most first 
courses in the subject, the authors suggest the following list 
of thirty-five experiments as affording a good training in those 

1 



2 GENERAL SUGGESTIONS 

fundamentals of the science most suitable for laboratory in- 
struction : 

Fundamental Course 

Mechanics: Exercises 3, 4, 8, 9, 10, 11, 19, 23, 25, 26, 27. 
Sou7id: Exercise 35. 

Light: Exercises 37, 38, 39, 42, 43, 46, 47.. 
Heat: Exercises 51, 58, 59, 61, 62. 

Magnetism and Electricity : Exercises 66, 68, 69, 70, 80, 81, 82, 
83, 84, 85, 89. 

The following ten exercises will supplement the above, 
particularly for those students whose ability enables them 
to do a maximum amount of work : 

Mechanics, 6, 13 or 14, 28, 29 ; Heat, 57 ; 
Sound, 34 ; Magnetism and Electricity, 72, 

Light, 44; 78 (or other experiment 

on resistance), 90. 

The following sixty exercises are suggested as a more 
extended course for those institutions favored with about 
double the laboratory time usually allotted to the first course: 

Extended Course 

Mechanics : Exercises 1, 3, 4, 6, 8, 9, 10, 11, 15, 16, 17, 19, 
20, 23, 24, 25, 26, 27, 28, 29, 30. 

Sound: Exercises 32, 34, 35. 

Light: Exercises 37, 38, 39, 42, 43, 44, 46, 47, 48. 

Heat: Exercises 51, 52, 57, 58, 59, 60, 61, 62, 63. 

Magnetism and Electricity : Exercises 65, 66, 68, 69, 70, 72, 
73, 78, 79, 80, 81, 82, 83, 84, 85, 86, 89, 90. 

The authors recommend the following list of experiments 
for girls, especially for those not intending to go beyond the 
high school. Most of these experiments have been selected be- 
cause of their close relationship to the practical affairs of life. 

Mechanics: Exercises 1, 2, 3. 6, 8, 9, 12 (or 13 or 14), 17, 18, 
23, 26, 27, 28. 



TO THE INSTRUCTOR 3 

Sound: Exercises 34 (or 35), 36. 
Light: Exercises 37, 38, 39, 49, 50. 
Heat: Exercises 51, 52, 59, 60, 61, 64. 

Magnetism and Electricity : Exercises 65, 68, 70, 79, 80, 82, 
83, 84. 

A number of interesting and valuable experiments do not 
appear in any of the preceding lists, but it is hoped that some 
of them will be taken from time to time either as substituted 
or as additional exercises. A limited amount of variation 
from year to year adds interest and vitality to any laboratory 
course. Many of the experiments just referred to will meet 
the needs of those instructors who desire to give more time to 
certain divisions of the subject. 

Order of Experiments. — The order in which the divisions of 
the subject are taken should depend upon the aim of the 
course and the conditions under which it is given. In their 
own work the authors find the most satisfactory order to be 
Mechanics, Heat, Sound, Electricity, and Light. In most 
syllabi, however, the subject of Light precedes that of Electricity. 
In the view of many, the experiments on Heat are best adapted 
to the student's powers after he has finished the experiments 
in Mechanics. 

Time required for Experiments. — A majority of the experi- 
ments are designed to take from 80 to 90 minutes of laboratory 
time, including the writing of the note-book record. Some of 
the shorter ones will require but half of that time, or a single 
school period. Even if a double laboratory period is not 
available for the longer experiments, the directions have been 
written so that the experiments can be done successfully in 
two single periods. The system recommended for the note- 
book record saves time in securing the observational data. 
Especial care has been taken not to overload the student with 
more manipulations and observations than would be reason- 
able for an average rate of work within the time allotment. 



4 GENERAL SUGGESTIONS 

The Experimental Directions 

Aim. — ■ At first sight it may seem that the directions for the 
experiments have been written in a rigid form which may 
hamper the individuality of the teacher using them. With 
the possible exception of the placing of the tables of observa- 
tions and calculated results, it will be found that the directions 
and their requirements are in accord with the usages which 
have become generally established as leading to intelligent and 
efficient laboratory work. 

The five main divisions of the printed directions are 
"Introductory/' "Experimental," "Calculated Results," "Dis- 
cussion," and "Conclusion." Certain suggestions as to these 
divisions appear in the paragraphs that follow. 

Introductory. — The paragraphs under this heading in the 
printed directions serve several purposes. First, they awaken 
the student's interest in the problem to be studied by reference 
to applications of Physics more or less familiar to him. Sec- 
ondly, the introductory statements show the relation between the 
practical applications and the laboratory problem to be solved. 
In some cases the paragraphs furnish a little theoretical in- 
formation, necessary for the intelligent performance of the 
experiment. All that is required of the student is that he read 
and understand this introductory matter — usually a task of a 
few minutes. It is not expected nor is it desired that the in- 
troductory matter be copied into the note-book. 

The authors offer no apology for the paragraphs introduc- 
tory to the experiments. They have simply put in written 
form those preliminary remarks that many instructors find 
desirable to make when the class assembles for the experiment. 
It is felt that the written form has the advantage of being al- 
ways available for the student's reference. 

Experimental. — Whenever the length and character of the 
experiment permits, the laboratory problem is presented as a 
whole to the student. With the general plan in mind, he is 
able to do the experiment with greater self-reliance and effi- 



TO THE INSTRUCTOR 5 

ciency than can be obtained from the slavish following of 
detailed directions with little grasp of their intent. 

In some experiments, however, detailed directions mnst be 
given to secure the successful imparting of a series of experi- 
mental facts. In such cases the divisions are made as few as 
possible and their meaning made clear by brief directions, a 
little supplementary information, and questions that the aver- 
age student should be able to answer from his experimental 
observations. 

The students are directed to place the data gathered in the 
experiment in a table of observations near the top of the left- 
hand page of the note-book record. The form for this table is 
usually furnished, and it is strongly recommended that the 
student write the form in the note-book before making any of 
the measurements. This procedure provides for the orderly 
recording of the data as soon as it is obtained, and insures the 
completion of the experimentation within the laboratory hour. 
There is economy also of the instructor's time, as he can 
quickly note the rate of progress of the individual and check 
inaccuracies in, the readings. 

With most experiments only one set of readings is indicated 
in the tables of observations, but the instructor desiring more 
can increase the number of columns at the right. In the 
opinion of the authors, much time is wasted by requiring the 
duplication of readings by the elementary student of Physics, 
unless in work where personal errors are large. 

Drawings. — After the observations are completed, the 
student is directed to make sectional or outline drawings from 
his apparatus so as to show that he understands its arrange- 
ment and operation. Many of the illustrations in this book 
have been made from drawings made by students in the regular 
course of their laboratory work. Such drawings will indicate 
to the users of this book the methods of representing labora- 
tory apparatus by simple outline drawings. The development 
of a simple scheme of sectional representation is within the 
power of any student and will prove most useful to him. 



6 GENERAL SUGGESTIONS 

Descriptions. — The table of observations and the sectional 
drawings render unnecessary long and elaborate descriptions of 
the experimental work. All that is asked is a brief but clear 
statement of the general method of the experiment and the 
recording of any experimental facts not shown by the draw- 
ings nor provided for in the table of observations. In the 
last few years it has become more and more recognized that 
the chief function of the laboratory note-book is to show the 
essentials of an experiment and not to provide useless drudgery 
for the student. 

Calculated Results. — Preceding the table of calculated results 
occurring in many experiments, are found directions for mak- 
ing the calculations. The authors have not hesitated to fur- 
nish information to aid the student in making the calculations 
when these are rendered more intelligible thereby. 

The directions call for the placing of the table of calculated 
results at the top of the right-hand page of the note-book record. 
The calculations themselves should be made directly below the 
table. These requirements secure prominent and convenient 
locations for the making of the computations and the orderly 
recording of the results. The student can tell from the tabular 
form what is expected of him in the way of calculations and 
knows when his work is finished. The instructor is enabled 
to check quickly the recorded results and to point out during 
the laboratory period sources of error. 

Discussions. — Under this division the student is directed to 
answer any italicized questions occurring in the experimental 
directions or the questions under the printed heading, Discus- 
sion. Thus the theoretical considerations of the experiment 
are brought together ready for reference or correction. 

Conclusions. — The student is either required to state for 
himself the formal conclusion justified by the experimental 
facts, or to complete a partial statement by filling in the in- 
dicated blanks. The latter method is preferred in those cases 
where a complete and well-worded conclusion is difficult for 



TO THE INSTRUCTOR 7 

the student to formulate. The vital part of the statement 
must be furnished by the student and requires thought on his 
part. 

Method of Laboratory Work. — Many of the advantages of 
having the note-book record follow a definite plan have been 
discussed under the topics preceding this. Tabular forms for 
the observations and the calculated results are appreciated by 
many instructors as leading to that economy of laboratory 
time which gives the best opportunity for experimentation and 
reflection. The forms for such tabulations may be written in 
the note-book prior to the laboratory hour and the general plan 
of the experiment studied. 

The authors believe that it is not only permissible, but highly 
desirable, for the student to know before he comes into the 
laboratory what he is to do. They require their own students 
to carefully study the experiment and to write the blank table 
of observations in the note-book before coming to the laboratory. 
Except in the case of very complicated experiments, the student 
is not allowed to have the experimental directions before him 
until he has taken all readings and completed his drawing and 
description. He is then allowed to refer to his direction sheet 
for guidance as to his calculations and conclusions. It has 
been found that under this plan the work in the laboratory is 
more intelligent and less of the " cook-book " order. Further- 
more, schools having only single laboratory periods may be 
certain of having the readings taken and the experiment 
described during the laboratory period, while calculated results 
and conclusions may be worked out the next day either in 
laboratory or classroom, or, if desired, done as part of the home 
lesson for the day following that of the laboratory period. 

No factor contributes more to the success of a laboratory 
course than having the apparatus tested and entirely ready for 
the student when he enters the laboratory. Then only is it 
possible for him to put the apparatus together and start its 
operation without loss of time, so that the readings can be 
made comfortably within the period. 



8 GENERAL SUGGESTIONS 

Note-book Directions. — On page 16 there will be found 
brief instructions intended for the student and relating to the 
form of the note-book record. Any orderly plan must have 
definiteness; so it becomes necessary to designate left-hand 
and right-hand pages for certain purposes. These directions 
may reverse the usage of some instructors, but it is hoped 
that they will realize it makes little difference whether the 
left-hand page or the right-hand page serves a certain purpose, 
so long as there is a definite systematic plan to make the note- 
book record a help to the student, and to make the ever present 
and laborious task of note-book correction easier for the 
instructor. 



DIRECTIONS TO STUDENTS 

Balances 

Construction of Platform Balances. — The platform balance 01 
trip scale is a simple, equal arm lever in which the vertical 
displacement of either arm is indicated by a pointer swinging 
across a horizontal scale. When the pointer swings approxi- 
mately equal distances on each side of the center division on 
the horizontal scale, the two lever arms are balanced and the 
scale is said to be in equilibrium. 




Fig. 1. Platform Balance. 

The construction of the trip scale is shown in Figs. 1 and 2 
on this and the following page. This convenient instrument 
for weighing is too often misused in the physical laboratory 
and poor results obtained with it. With the observance, how- 
ever, of a few simple precautions, rapid, accurate weighings 
can be made with this piece of apparatus. 

Adjustment of Platform Balances. — Before weighing always 
see that both platforms are clean. Then touch lightly one 

9 



10 



GENERAL SUGGESTIONS 




Fig. 2. Sectional View of Balance. 



platform and note ' whether or not the pointer swings freely 
and equally on each side of the center line of the scale. The 
pointer should oscillate at least two divisions to the right and 
to the left. In too short swings the friction in the bearings 

makes the scale rela- 
tively less sensitive. 
Therefore the point- 
er's coming to rest at 
the center point is no 
sure indication that 
the two arms of the 
scale are balanced or 
in equilibrium. 

In case the pointer 
swings to a distinctly 
greater distance on 
one side of center, 
turn the thumb nut which is just below the center, so that the 
nut moves a little distance towards the side of the lesser swing. 
Again note the swings. When they are approximately equal 
on both sides of center, the scale is adjusted for weighing. 

Handling of Weights. — Place the object to be weighed on 
the left-hand platform or pan and the weights on the right-hand 
platform. In adding or removing weights, prevent with the 
left hand the movement of the pans until the change of 
weights has been made. In this way avoid jarring the balance 
and injuring the knife-edges. 

For the first weight select the one which in your opinion is 
about equal to the object being weighed. If this weight is too 
small, take it off and replace it with the next larger one. 
Continue in this way until you have the largest weight which 
is lighter than the object. Then add the next smaller weight. 
Time-saving weighing means the systematic use of the next 
smaller or the next larger weight, as the case may be, until 
the scale is balanced. 

In practice the graduated beam with its rider enables one to 



TO STUDENTS 11 

dispense with the smaller weights. If the beam is graduated 
for 5 grams, the 1-gram and the 2-gram weights are not used ; 
with a 10-gram beam, the weights below 10 grams are not 
necessary. By means of the graduated beam, these smaller 
weights are found by moving the rider to the right until the 
balance is in equilibrium. Note carefully on which side of 
the rider the reading should be made, and remember that 
the reading can be made to tenths of a gram. 

When the correct weight is obtained, count carefully the 
weights on the right-hand pan and add the weight indicated 
on the beam. Record this total weight at once in the labora- 
tory note-book. 

Eeturn the weights to their block, or case, counting as you 
do so. Add the weight indicated on the beam and check the 
weight recorded in the note-book. Remove the object from- its 
scale pan. A scale left with the arms unequally balanced soon 
loses its sensitiveness, owing to unnecessary wear on the 
bearings. 

Beam Balances. — Another form of balance much used in the 
physical laboratory is the beam balance. The beam in this 
case rests at its center point on a knife-edge, or a wedge, sup- 
ported on a vertical stand. Pans are suspended on the ends 
of the beam either by hooks, or in the more expensive kinds by 
stirrups which rest on knife-edges. A vertical pointer indi- 
cates on a small graduated scale the oscillations of the beam. 
Some beam balances have on one arm of the beam a rider, 
which slides along a graduated scale and thus indicates the 
smaller weights. To avoid dulling the knife-edges, there is 
often a device which lifts the beam off the knife-edges when 
the balance is not in use. The pan arrest similarly lifts the 
bow and stirrup suspension from off the knife-edges on the 
ends of the beam. 

The specific gravity balance is usually a beam balance which 
has a shorter suspension for one of the pans. From a hook on 
the under side of this pan are suspended objects which are to 
be weighed in a liquid. 



12 GENERAL SUGGESTIONS 

The hornpan balance is simply a beam balance, which is sup- 
ported vertically from a hook hung on a ring stand or held by 
the hand. 

Spring Balances. — A spring balance measures the mass of a 
body by the elongation of a spiral spring. The weight is in- 
dicated on a graduated scale by a pointer attached to a draw- 
bar on the free end of the spring. Attached to the drawbar 
is a hook on which is suspended the object to be weighed. 

The spring balance is made to read correctly in vertical 
position, with the hook downward. The weight of the draw- 
bar and hook should be sufficient to bring the pointer to 
the zero mark on the graduated scale. If the pointer does 
not stand at zero with no load on the balance, a correction 
must be made to the weight registered on the scale in order to 



L &-"- u -*^tv 



get the true weight of the object. The inconvenience of mak- 
ing these corrections may sometimes be avoided by wrapping 
about the shank of the hook a strip of sheet lead, sufficient in 
weight to bring the pointer to the zero point of the scale. 

The friction in a spring balance tends to make less accurate 
the readings in the first portion of the graduated scale. At the 
other end of the scale, when the spring is near its maximum 
stretch, the elongations are not quite proportional to the 
heavier weights added. Accordingly the most accurate read- 
ings with a spring balance are those obtained in about the 
middle portion of the graduated scale. 

In some experiments the spring balance is used to measure 
the pull or force exerted upon its spring. When used for this 
purpose it is termed a dynamometer. 

Sensitiveness of a Balance. — The sensitiveness of a balance 
may be defined as the smallest difference which is indicated 
by the balance with a given load. The trip scale should be 
sensitive to at least the tenth of a gram with an ordinary load, 
i.e. show a difference between 50.6 and 50.7 grams. A good 
hornpan balance indicates weights within the hundredth of a 
gram (1 centigram) while an accurate chemical balance is sen- 
sitive to a ten-thousandth of a gram (tenth of a milligram). 



TO STUDENTS 13 

Relative Advantages of Platform and Beam Balances. — The 

platform balance, while it is easy to keep clean and can stand 
much usage, is usually not so sensitive as the beam balance. 
The broad platforms, however, are very convenient for weigh- 
ing bulky, unstable objects, and the oscillations of its beam 
are easily controlled. 

The sensitiveness of a beam balance is gained at the expense 
of stability and durability, for the beam is easily displaced and 
the knife-edge suspension becomes dulled by use. On this ac- 
count great care should be taken not to jar the balance nor 
allow the beam to oscillate too rapidly. The weights should 
be placed gently upon the pans and removed when the pans 
are at rest (i.e. supported by the pan arrest or by the hand). 

Were it not for the awkwardness and carelessness of some 
students, the beam balance would always be most desirable for 
rapid, accurate weighings in the physical laboratory. 

Electrical Measuring Instruments 

The instruments used for measuring the strength or the 
pressure of an electric current have very delicate parts and 
may be easily ruined by either rough usage or excessive 
current. 

Before using any galvanometer or other meter the student 
should assure himself that it has the proper scale range and 
current-carrying capacity for the work in hand. He must 
further so connect his apparatus that the instrument will not 
be upset or pulled out of place by any change in connections 
made during the experiment. As the several instruments that 
the student may be called to use in his experiments differ in 
their sensitiveness, method of connection, and method of read- 
ing, each kind will be briefly discussed by itself. In reading 
all instruments, tenths of the smallest divisions should be esti- 
mated. 

Tangent Galvanometer. — This consists of a compass needle 
mounted at the center of a hoop, on which is wound the wire 



14 GENERAL SUGGESTIONS 

which is to convey the current. This is the most rugged of 
the instruments, but the pivot is likely to be bent by dropping 
or violently jarring the instrument. Where there are a num- 
ber of binding posts, to permit the use of different numbers of 
turns of wire, find out from the instructor which posts to use 
and the number of turns of wire included between them. In 
order to read the instrument accurately, it should be so placed 
on the table that it will be possible to look directly down on 
the needle. The instrument should be carefully turned until 
the needle is in the plane of the coil. 

D'Arsonval Galvanometer. — The moving part of this instru- 
ment is a light coil of wire, suspended between the poles of a 
permanent magnet by a fine wire or ribbon through which the 
current passes. This suspension is exceedingly thin, so that 
even a slight shock to the instrument will break it and a 
comparatively small current will melt it. The instrument is 
commonly provided with a clamping device which takes the 
weight of the coil off the suspension when the galvanometer is 
not in use. 

In setting up the galvanometer, keep the coil clamped until 
you are ready to connect to the source of current. Then make 
sure that the instrument is leveled in such a way that the coil 
does not rub against any part of the instrument but hangs per- 
fectly free. The method of reading the deflections for the 
particular instrument you are using will be explained by the 
instructor. 

It is exceedingly important that only a very small current 
pass through the coil of the instrument. On this account, the 
galvanometer should have either a coil of high resistance in 
series with it or a low resistance shunt across the terminals for 
most experiments. Such additions to the instrument should 
be made either by the instructor previous to the laboratory 
hour or under his immediate direction by the student. 

Ammeter. — The commercial form of this instrument is 
usually a d'Arsonval galvanometer provided with a shunt of 



TO STUDENTS 15 

such resistance that the deflections of the needle give the num- 
ber of amperes directly. The coil is pivoted instead of being 
suspended, but the instrument must be guarded against falls 
and shocks just as a fine watch would be. 

Before connecting the ammeter in circuit, be sure that its 
range is sufficient for the current to be measured. If the in- 
strument has more than one range, always connect for the largest 
range first, and then change the connections to those for a 
smaller range, if the readings indicate that this can be safely 
done. 

If the ammeter has an external shunt, be sure that the con- 
nections between the shunt and the instrument movement are 
tight. A loose contact will certainly make an incorrect read- 
ing and may burn out the instrument. 

Connect the terminals of the instrument in series with the 
circuit. If connected in shunt with the other apparatus, the 
resistance of the instrument is so small that the movement will 
probably be burned out. 

In every electrical circuit, there should be a switch that can be 
opened instantly if there is the slightest indication of too much 
current for the instruments or any other part of the apparatus. 

Voltmeter. — This is similar to the ammeter in construction, 
but has a high resistance in series with the movement instead 
of a shunt across the movement. The voltmeter measures 
pressure, while the ammeter measures current flow. 

The same precautions for handling and for the selection of a 
proper scale range are to be observed as in the case of the am- 
meter. 

Connect the voltmeter across (in shunt with) the circuit or 
that part of the circuit in which the voltage drop is to be 
measured. 

Resistance Box. — The voltage applied to a resistance box 
should never be great enough to cause more than 0.1 ampere to 
pass through the box. 



16 GENERAL SUGGESTIONS 

The Laboratory Note-book 

Unless other directions are given by the instructor, the fol- 
lowing plan should be followed in recording experiments in 
the note-book. 

Number of Experiment. — Place to the left and at the top of 

the left-hand page. 

Date of Experiment. — Place to the right and at the top of 

the left-hand page. 

Title. — Place immediately below the number and date. 
Object. — Place directly below the title. 

Tables of Observations. — Place immediately below the object. 
In case the instructor desires the duplication of the observa- 
tions, make the necessary number of parallel columns at the 
right. Always record the measurements, as soon as made, in 
the tabular form. Decimals should be used, rather than com- 
mon fractions. 

The number, the date, the title, the object, and the table of 
observations should be written in the note-book before the 
experimental work is begun. 

Drawings. — Place on the left-hand page clear sectional 
drawings showing the arrangement and operation of your ap- 
paratus. In making a sectional drawing, imagine a vertical 
plane passing through the middle of your apparatus ; then 
imagine your paper to be in the position of this plane. Draw 
lines where the paper would touch the intersected apparatus. 

Descriptions. — Place these usually on the left-hand page and 
shorten your work by referring to your drawings. A simple, 
clear account of the general method of the experiment is prefer- 
able to an elaborate description. 

Table of Calculations. — Place at the top of the right-hand 
page before making any of the calculations. Do the mathe- 



TO STUDENTS 17 

matical work involved, immediately below the table, and record 
the results as soon as obtained in the tabular form. 

Discussion. — -Under this heading on the right-hand page, 
answer any italicized questions occurring in the experimental 
directions as well as the questions under the printed heading 
of " Discussion." If more room is necessary, continue on the 
next right-hand page. 

Conclusion. — Place under this heading on the right-hand 
page, immediately following the Discussion. 

Introductory. — It will pay yon to read and understand this, 
before beginning the experimental work. It is not to be copied 
into the laboratory note-book. 



LABORATORY EXERCISES 



EXPERIMENT 1 

Metric Units of Measurement 

OBJECT. To become familiar with the units of metric measure- 
ments commonly used in scientific work. 

Apparatus. Meter stick; scissors; small graduate (50 or 
100 c.c); large graduate (500 or 1000 c.c); liquid quart meas- 
ure; small wide-mouth bottle; tumbler; platform balance ; metric 
weights; 1 lb. weight. 

Material. "Oak tag," or some other kind of stiff paper; 
mucilage, or paste. 

Introductory : 

The Metric System is the official system of units of 
measurement in most civilized countries. It is the system 
used in scientific work in the United States. The unit 

100 MILLIMETERS — 10 CENTIMETERS = 1 DECIMETER = 3. 937 INCHES. 



1 


2 


3 


4 


5| 6 

I I I 


7 


8| 


9 10 


















I ' i 




I II I 


1 1 J I 


II I Mill I 


TE 


MM 


III 


MUM 


Mill I II li 


I II I I II I 


n ii i i i ii 


II I II I I I II II I 


MM 


1 1 1 1 1 1 1 1 II 




I 




I I I I 




I I I I I I I I I 


I I I I | I I I I 


I I 


I 


I I I I 












1 


2 


3 


4 



INCHES AND TENTHS 



Fig. 3. 



of this system is the meter, and standard bars with this 
distance marked on them are preserved for reference by 
various governments. 

The Metric System is a decimal system and therein 
lies its great convenience. The meter is subdivided into 

18 



METRIC UNITS OF MEASUREMENT 19 

ten parts, each of which is termed a decimeter ; the hun- 
dredth of a meter is a centimeter ; the thousandth of a 
meter, a millimeter. From these fundamental units, the 
units of surface, volume, and weight are derived. 

The meter measures 39.37 inches. 

Experimental : 

At the top of the left-hand page of the laboratory note- 
book put the number and title of the experiment and the 
date. Then state the object of the experiment. Immedi- 
ately below this, put the following tabular form for the 
readings : 

Observations 

Length of note-booh cover ....... cm. 

Width of note-book cover ....... cm. 

Metric equivalent of liquid quart . . . . cm. s 

Capacity of small bottle cm. 3 

Capacity of tumbler cm. 3 

Weight of note-booh g. 

Metric equivalent of a pound g. 

Units of Length. — (a) Examine a meter stick, noting 
its subdivisions. In your laboratory note-book, just below 
the table of observations, rule horizontal lines of the fol- 
lowing lengths, labeling each line with its length : 

1 decimeter, 1.1 decimeters, 1.5 decimeters, 5 centimeters, 
2.5 centimeters, 1.3 centimeters, 1 centimeter. 

(5) Measure in centimeters and tenths of a centimeter 
the length of the cover of your laboratory note-book. 
Similarly measure the width. Record the dimensions. 

Units of Volume and Capacity. — (tf) On a separate 
piece of paper, lay off a diagram like Fig. 4. 



20 



LABORATORY EXERCISES 



r 

i 


t. 






t. 

S 






<— i cm— > 


T 


< — 1 cm— > 


*£ 1 CW— > 




t 








i 








y 







Cut aroand the diagram with a pair of scissors. Bend 

over the little flaps and fold into a cube, pasting the 

/~—\ flaps on the inside so as to 

hold the cube together. 

The little cube, if accu- 
rately made, is a cubic centi- 
meter, the unit of volume. 
1000 cubic centimeters give 
the liter, the unit of capac- 



Fig. 4. 



ity. For convenience, the 
measuring instruments for 
liquids are usually cylindri- 
cal vessels, marked off in 
cubic centimeters and 
known as graduates. 

(d) Using a large gradu- 
ate, determine how many cubic centimeters of water are 
needed to fill an ordinary quart measure. 

(To be done in groups of four students unless otherwise directed 
by the instructor.) 

(e) Using a small graduate, find the capacity in cubic 
centimeters of the small bottle furnished you. 

Similarly determine the capacity of an ordinary drink- 
ing tumbler. 

Units of Weight. — The weight of a cubic centimeter 
of water at its maximum density (4° C.) is taken as the 
unit of weight, the gram. 

1000 grams make a kilogram, a weight used for measur- 
ing large quantities. 




Fig. 5. Dissected Liter Block. 



PROPERTIES OF MATERIALS 21 

(f) Using a platform balance, find the weight in grams 
of your laboratory note-book. Record. 

(^) Determine how many grams are needed to counter- 
balance an ordinary pound weight. Record. 

Tables for the calculated results should be placed at 
the top of the right-hand page of the note-book, and the 
calculations worked out just beneath them. 

Express the number of cubic centimeters found in (d) 
as the decimal part of a liter. Using this number, calcu- 
late the equivalent of a liter in quarts, carrying the result 
to two decimal places. 

Calculate from the comparison of weights found in (^), 
the equivalent of a kilogram in pounds and tenths of a 
pound. 

Calculated Results 

1 liter qts. 

1 kilogram lbs. 

Discussion : 

In what respects was the convenience of the Metric 
System shown in your measurements ? Place the answer 
to this question on the right-hand page of the note-book, 
heading it " Discussion." (Under this heading are to be 
written the answers to any italicized questions occurring 
in the experimental directions.) 



EXPERIMENT 2 

Properties of Materials 

OBJECT. To examine a few common substances so as to deter- 
mine their properties. 

Apparatus. Triangular file ; pocket-knife ; hammer ; anvil, or 
flatiron (with detachable handle). 



22 



LABORATORY EXERCISES 



Material. Copper wire #18, or some larger size; strips of 
sheet lead about 3±" X \"\ pieces of small glass tubing ; paraf- 
fin ; rubber bands, or strips of sheet rubber ; steel nails. 

Introductory: 

Every substance has its own set of properties. Certain 
of these are the well-marked or characteristic properties 
by which we recognize the substance. These characteristic 
properties are important in that they determine the prac- 
tical use of a substance. 

Experimental: 

The substances to be examined are copper, glass, rubber, 
lead, paraffin, wood, and steel. Take them in any order. 
Tabulate on the left-hand page of your note-book the 
results of your examination, in a table like that given 
below. 



Substance 


Hardness 


Lustre 


Malleability 


Elasticity 


Copper 










Glass 










Rubber 










Lead 










Paraffin 










Wood 










Steel 













PROPERTIES OF MATERIALS 23 

Hardness. — Use a knife blade or a file to determine 
the hardness. Describe this in comparative terms, as 
very soft, soft, somewhat hard, hard, and very hard. 

Lustre. — Note two kinds of lustre or " shine." Which 
substances would be said to be without lustre ? 

Malleability. — Use a hammer, and tap the substance 
on an anvil or other block of iron to ascertain whether or 
not the substance can be hammered out into sheets with- 
out breaking. 

Elasticity. — Try to change the shape of the substance 
by bending. If the substance bends or gives, remove the 
strain to find out whether or not the substance will return 
to its original condition. In determining the elasticity, 
make use of the results obtained in testing for malleability. 

Ductility. — A ductile substance admits of being drawn 
out into fine wire. This property is not easily determined 
in the laboratory by students. Which of the substances 
are ductile ? Why do you think so ? Do not tabulate for 
ductility. 

Write a simple description of how you determined each 
of the properties tabulated. No drawing is necessary for 
this experiment. 

Discussion : 

Under this heading on the right-hand page of note- 
book, answer any italicized questions occurring in the 
experimental directions, and also the following questions: 
Which of the substances are good conductors of heat? 
Of electricity ? Name any other general properties that 
have not been mentioned in this experiment (Class 
Discussion). 



24 LABORATORY EXERCISES 

EXPERIMENT 3 

Measurement of Bodies 

OBJECT. To find in metric units the volume of a block of wood. 

Apparatus. Wooden block ; metric scale. 

Introductory : 

Iron is " heavier" or more dense than wood. To find 
out how many times as dense, measurements must be made 
of the size and weight of a piece of each. It is more con- 
venient in physical work to make the measurements in the 
metric system, because it is a decimal system. The chief 
units used are the centimeter and the gram. 

Experimental : 

On the left-hand page of your note-book and immedi- 
ately below the statement of the object of the experi- 
ment, put a tabular form like the following for the 
measurements to be made: l 

Observations 

Number of block 

Length of block cm. 

Width of block cm. 

Thickness of block cm. 

When the scale is placed so that the scale divisions touch 
the block, there will be less error in reading measurements. 

x Note to Instructor. Many teachers find it desirable to have the 
students write in their laboratory note-books, previous to coming into the 
laboratory, the number, the title, and the object of the experiment, and 
any tabular form of measurements to be made. As this will be the first 
experiment in many courses, the directions for the note-book record have 
been made very definite. 



MEASUREMENT OF BODIES 



25 



mrv 



ll|llli|HI!|!lli|llll|!ll 

2 3 



5 



I 



Fig. 6. 



The eye must be directly in front of the point on the scale 
and the point located in the block. Why is it desirable 
to estimate to hundredths of a division on a scale divided 
into tenths? 

Using the scale in this 
way, find the length, 
breadth, and thickness of 
the block furnished you. 
Do not make measure- 
ments at bruised corners. 

From your apparatus 
make, on the left-hand page of the note-book, an outline 
drawing similar to that given (Fig. 6). 

On the same page write a brief description of what you 
did, touching on the points regarding measurements which 
you were instructed to observe. Complete in the laboratory 
at least the drawing and the description. The left-hand 
page of the note-book should be finished before the right- 
hand page is begun. 

On the right-hand page, place the table of calculated 
results, the calculations themselves, the answers to the 
questions for discussion, and the formal conclusion. The 
tables of calculated results should always be placed at the 
top of the right-hand page. 



Calculated Result 



Volume of block 



cm. 



In making the calculations for the above results, indicate 
the units of measurement for each result. Do not carry 
out the calculated volume beyond the hundredths of a 
cubic centimeter. Read the discussion on " Significant 

Figures," pages 27-29. 



26 LABORATORY EXERCISES 

Discussion : 

Under this heading on the right-hand page answer any 
italicized questions occurring in the experimental direc- 
tions. Why would it be desirable to make several meas- 
urements of each dimension of the block and take the 
average for the calculation ? 

Conclusion : 

The volume of block No. is cm. 3 . 



SIGNIFICANT FIGURES 

Accuracy in Scientific Calculations. — Calculations in scientific 
work are based on readings obtained by some method of meas- 
urement. The calculations cannot be more accurate than the 
figures with which they are made. Yet beginners in physics, 
in their zeal to be accurate, retain figures in their calculations 
far beyond the point justified by the accuracy of the measure- 
ments. The results are not so accurate as they would be 
if certain figures had been discarded in the progress of the 
calculations. The following paragraphs aim to show how 
scientific accuracy may be obtained in the calculations of 
experimental physics. 

Average Readings or Results. — The dimensions of a rectan- 
gular block may be measured with a metric scale graduated in 
centimeters and millimeters. By estimating the tenths of a 
millimeter, the readings may be expressed to the hundredths 
of a centimeter. 

The following readings might be obtained for the length of 
the block as determined along two of its edges : 

B 

7.45 cm. 
7.42 cm. 
7.47 cm. 





A 






7.45 


cm. 




7.42 


cm. 




7.47 


cm. 


3) 


22.34 


cm. 




7.44 


cm. 



3 )22.34 c m. 
7.446 cm. 

(Correct scientific average.) (Incorrect scientific average.) 

The second decimal place in these readings represents the 
estimated tenths of a millimeter. In estimating such small 
quantities, one may readily misjudge not only by one tenth of 

27 



28 LABORATORY EXERCISES 

a millimeter, but even to the extent of two or three tenths. 
Hence the figures expressing tenths of a millimeter are not 
accurate, but are doubtful figures. They are indicated here in 
heavy-face type. 

In column B the average given for the three readings is 
7.446. In this number the second 4 is a doubtful figure, there- 
fore the 6 in the next decimal place beyond must be more than 
doubtful. This figure 6- means nothing in our units of meas- 
urement. 

Some authorities may claim that 7.45 is nearer to the correct 
average in such a case. Mathematically this is so, but it must 
be remembered that one cannot judge accurately between 0.04 
cm. and 0.05 cm. on a scale whose smallest division is 0.1 cm. 
Hence the average of 7.44 in column A may be regarded by 
the painstaking student as correct and reasonable, particularly 
as the divisor is a small number. 

Retention of Significant Figures. — Let us find the volume of 
a rectangular block with the following dimensions : length, 
7.44 cm. ; width, 4.67 cm. ; and height, 2.82 cm. To find the 
area of the base multiply the length by the width, indicating 
the doubtful figures in heavy-face type. 

7.44 
4.67 



5208 

4464 
2976 
34.7448 cm. 2 

In the first partial product, 5208, all the figures are doubt- 
ful, as they were obtained by multiplying by the doubtful 
figure 7; in the second partial product, 4464, the final 4 is 
doubtful because it resulted from a multiplication in which a 
doubtful figure was a factor ; and for the same reason the 6 in 
the third partial product, 2976, is doubtful. 

In the addition of the partial products, figures which are ob- 



SIGNIFICANT FIGURES 29 

tained by adding doubtful figures, are doubtful figures. This 
makes the last four figures doubtful in the total 34.7448. All 
the doubtful figures but the first should be discarded. Then 
the area of the base as justified by the accuracy from measure- 
ments is 34.7 square centimeters. 

To find the cubical contents multiply the area of the base by 

the height : 

34.7 

2.82 

694 

2776 

694 



97.854 cm. 3 

Discarding all the doubtful figures except the first, 97.8 cm. 3 is 
the correct volume of the rectangular block. 

A student who found the cubical contents without discard 
ing any of the doubtful figures would get as a result 97.980336 
cm. 3 . Not only would he have done extra work, but his result 
would not be scientifically accurate. 

A good rule in making calculations is to retain only signifi- 
cant figures. Significant figures include the first doubtful 
figure and the figures preceding it. 



30 



LABORATORY EXERCISES 



EXPERIMENT 4 



Volume Measurement of an Irregular Body 



OBJECT. To find the volume of a body of irregular shape. 

Apparatus. Solid of irregular shape , as a lump of metal, 
brass hook weight (50 or 100 g.), or large-sized lead sinker; 
cylindrical graduate (100 c.c.) ; strong thread, or string. 

Introductory : 

The volume of a body of irregular shape cannot be 
found by measuring a few dimensions and then making a 
simple calculation. A stone dropped into a glass of water 
raises the water level. As the stone and the water can- 
not occupy the same place at the same time, the volume 
of the stone may be found from the increase in volume. 

Experimental : 

Given a lump of metal and a graduated cylinder with 
water in it, devise a way of getting the volume of the 
metal. 




^ 



100-^1 
95 
90^ 



1~. 






^_ 




Fig. 7. 



MEASUREMENT OF AN IRREGULAR BODY j 31 

In reading a graduate, place the eye on the level of the 
lowest point of the curved surface and record this as the 
height of the water. As the graduations are cubic centi- 
meters, and as an error of 1 cm. 3 in the volume that we 
are measuring would be a considerable per cent of error, 
therefore, estimate tenths of a cubic centimeter as nearly 
as you can. 

Make the readings indicated by the table of observations 
and record in a similar tabular form near the top of the 
left-hand page of note-book. 

Observations 

Reading before immersing the metal . . . cm? 

Reading after immersing the metal .... cm. s 

Number of lump of metal 

Material of lump 

On the left-hand page of the note-book, make from 
your apparatus, outline drawings similar to Fig. 7, and 
write a simple description of the experimental method 
used. 

Discussion : 

What property of matter makes possible this method 
of finding the volume ? 



Conclusion : 

Volume of lump of metal No. is cm. 

cm. 3 = . ..cm. 3 . 



3 __ 



32 



LABORATORY EXERCISES 



EXPERIMENT 5 



Density 

OBJECT. To determine the density of wood and of metal. 

Apparatus. Block used in Experiment 3 ; lump of metal 
used in Experiment 4 ; spring balance or other balance ; linen 
thread. 

Introductory : 

Iron is heavier than wood and lead is heavier than iron. 
By this we mean that, if we take pieces of the three 
materials of the same size, the lead has the greatest 
weight, and so we conclude there are more pounds per 
cubic foot (or grams per cubic centimeter) of lead than of 
iron or of wood. That is, the lead has the greatest den- 
sity, for density is the mass per unit volume of a sub- 
stance. In the metric system this is written grams per 

cubic centimeter or ^* ■ 



o 




Fig. 8. 



cm.° 

Experimental : 

All that is necessary for the calcu- 
lations is to know the mass and vol- 
ume. The volume of each of the solids 
to be used has already been obtained 
in Experiments 3 and 4. 

The mass of a body is measured by 
its weight. The greater the mass, the 
more a body will stretch a spring from 
which it is hung. The graduations on 
the scale of the spring balance indicate 
the masses that must be hung upon 
the hook, in order to pull the pointer 



DENSITY 33 

to each division on the scale. The mass of the block may 
be found, then, by hanging it upon a spring balance. 
Read the balance to tenths of the smallest division. 

If a beam or a platform balance is used, read on page 
11 or on page 9 the directions for its use before perform- 
ing this experiment. 

Observations 

Mass of wood g. 

Mass of metal . g. 

From your apparatus make, on the left-hand page of the 
note-book, an outline drawing like Fig. 8. On the same 
page write a simple description of what you did.' 

Make the calculations and put the results in a table at 
the top of the right-hand page of the note-book. 

Calculated Results 

Volume of block (from Exp. 3) . cm? 

Volume of metal (from Exp. 4) .... cm? 

Density of wood g. per em? 

Density of metal ( ) g. per cm? 

Conclusion : 

The density of wood is 

The density of is 

(name metal) 



34 LABORATORY EXERCISES 

EXPERIMENT 6 

Elasticity — Hooke's Law 

OBJECT. To find the relation between the elongation of a spiral 
spring and the stretching force, provided the elastic limit is not ex- 
ceeded. 

Apparatus. A closely coiled spiral about 10 cm. long and 
1.7 cm. in diameter, made of #20 spring brass wire, with a hook 
and pointer at one end and at the other a straight section for 
hanging or clamping ; stand with pendulum clamp and meter stick 
clamp ; meter stick ; pan for suspension ; metric weights. 1 

Introductory : 

When a steamboat makes its landing, the large hawsers 
tighten as the boat is swung toward the wharf. The 
diameter of the large rope becomes smaller and measure- 
ments would show the length had been stretched. The 
stretching force has changed both the shape and volume 
of the rope. When the the line is cast off again, the rope, 
because it is an elastic body, recovers very nearly its origi- 
nal diameter and length. Sometimes the stretching force 
is so great that the rope snaps because the ultimate strength 
of the rope has been exceeded. 

In materials subjected to stretching forces, as the wire in 
the coil of a spring balance, the change in diameter is very 
slight, but there is considerable lengthening or elongation. 
The question arises whether the elongation proceeds irregu- 
larly or at a uniform rate as the stretching force increases, 
provided the elastic limit of the material is not exceeded. 

1 The spiral coil may be conveniently made by winding the wire around 
a J" pipe. The special pendulum and meter stick clamps may be replaced 
with ordinary laboratory clamps or other attachments. In case weights 
heavier than those specified for the loads are used, a larger size of wire 
should be selected. 



ELASTICITY — HOOKE'S LAW 



35 



Experimental : 

Place the meter stick in a vertical position. Suspend 
the weight pan on the hook of the spring 
and attach the pointer just above the 
hook at right angles to the spring. Sus- 
pend the spring so that the end of the 
pointer is close to the metric scale, but 
does not touch it. Also try to adjust the 
position of the spring so that the pointer 
is opposite some main division of the metric 
scale such as the 10-cm. or 20-cm. mark. 
This mark is the zero reading or the 
point from which the first elongation is to 
be measured. Record this zero reading. 

Put a 5-gram weight in the pan and 
read the position of the pointer. Take 
off this weight and allow the spring to 
go back. Again read the position of the 
pointer. Now put on the 10-gram weight. 

Observations 




Fig. 9. 
Continue in 



Load on Pax 


Reading of 
Pointer 


Zero Reading 


Corrected Reading 
(Total Elongation) 


5 grams 


cm. 


cm. 


cm. 


10 grains 


cm. 


cm. 


cm. 


15 grams 


cm. 


cm. 


cm. 


20 grams 


cm. 


cm. 


cm. 


25 grams 


cm. 


cm. 


cm. 


30 grams 


cm. 


cm. 


cm. 


35 grams 


cm. 


cm. 


cm. 


40 grams 


cm. 


cm. 


cm. 


45 grams 


cm. 


cm. 


cm. 


50 grams 


cm. 


cm. 


cm. 


55 grams 


cm. 


cm. 


cm. 


60 grams 


cm. 


cm. 


cm. 



36 LABORATORY EXERCISES 

this manner, increasing the load 5 grams at a time and 
recording the results in tabular form near the top of the 
left-hand page. The total elongation due to the load is 
the difference between the pointer reading and the zero 
reading which is made each time. 

Make a drawing from your apparatus, and write a sim- 
ple description of the experimental method. 

Curve on Cross Section Paper. With the loads taken 
and the total elongations obtained, plot a curve on cross 
section paper, placing loads on the perpendicular axis and 
total elongations on the horizontal axis. Attach the cross 
section paper by one edge to the right-hand page of note- 
book. 

Discussion : 

AVhat kind of a curve is obtained ? What relation does 
this show between the total elongation and the stretching 
force ? How elastic should the spring be in order to obtain 
very exact results ? Was your spring such a spring ? 
What is the principle upon which a spring balance works ? 

Conclusion : 

Complete the following statement of Hooke's Law : 
When the elastic limit is not exceeded, the distortion of 

a body due to a stretching force is to the 

force. 



TENACITY OF WIRE 



37 



EXPERIMENT 7 

Tenacity of Wire 

OBJECT. To determine (a) the relation between the tension 
and the elongation of a wire; (&) the comparative tenacity of 
copper, iron, and brass. 

Apparatus. Block for clamping wire ; pulley with stem ; 
thumb tacks ; weight carrier; slotted weights — 1 lb., 2 lb., 2 lb., 
5 lb., 10 lb.; millimeter scale ; large-sized needle ; magnifier (a 
cheap convex lens may be used). 

Material. Spools of iron, brass, and copper wire, $ 28; 
sealing wax. 

Introductory : 

When a load is suspended by means of a cord, the cord 
stretches. As the suspended weight is increased, the cord 
stretches further until it finally breaks. A wire or a metal 
rod behaves in the same way, but the elongation is smaller 
and not so readily noticed. There is, however, definite 
elongation. This must be allowed for in the construction 
of bridges and other structures. By experimenting with 
fine wire under increasing loads, we can follow all the 
changes until the wire breaks. 




^/l/^^lllilinllhl^^^m^ 



Fig. 10. 




38 



LABORATORY EXERCISES 



Experimental : 

(a) The block is clamped to one end of the laboratory 
table and the stem of the pulley set into a hole bored 
diagonally into the opposite end. 

A piece of wire about 30 cm. longer than the table is cut 
off. This is clamped to the binding post, given a turn around 
the wooden cylinder, and attached to the weight carrier at 
the other end. Care must be taken that there are no kinks 
or sharp bends anywhere in the wire. The wire is then 
placed over the pulley and the needle attached at right an- 
gles to it with a drop of melted wax at a point near the pulley. 

The millimeter scale is then fixed in place beneath the 
the needle with the thumb tacks so that its divisions are 
parallel to the needle. 

A 2-lb. weight is next placed on the carrier to straighten 
the wire ; then it is removed and the zero reading of the 
needle taken, tenths of the smallest scale division being 
estimated. A lens may be used to advantage in estimating 
tenths. 

Weights are now added, a pound at a time, the amount 
of stretching force and the reading of the needle on the 
scale being noted and immediately recorded in tabular 
form near the top of the left-hand page. 

After each reading remove the weights and again note 
the zero reading. The force which causes the first con- 
siderable shifting in the zero point is known as the elastic 
limit. Continue the readings until the wire breaks. 



Observations on 



Wibe, Gauge No. 



Stretching Force 


Zero Reading 


Reading of Pointer 


Breaking Strength 


etc. 


etc. 


etc. 


etc. 



TENACITY OF WIRE 39 

(5) Replace the broken wire with another of different 
material, and add the weights one pound at a time until 
the wire breaks, without recording the elongations. Re- 
peat with as many wires as the instructor may designate. 
Record results in tabular form on the second left-hand 

page. 

Observations, Part (5) 



Material of Wire 



Gauge Number 



Breaking Strength 



On the left-hand page of the note-book make a simple 
drawing of your apparatus, and write a simple description 
of how the experiment was done. 

On the right-hand page, at the top, place the calculated 
results for Part (a) in tabular form. 

Calculated Results 

Stretching force 1 lb. 2 lb. 3 lb., etc. 

Elongation mm. ._„__. mm. mm., etc. 

Curve. — On a piece of cross section paper, plot a 
curve, laying off forces as abscissae (horizontal) and 
elongations as ordinates (vertical) to the scale given by 
the instructor. Compare the force at the point where the 
curve begins to turn with the elastic limit. Paste the cross 
section paper by one edge into the note-book. 

Discussion : 

Does the wire follow Hooke's Law in that u the dis- 
tortion (elorgation) is proportional to the stretching 
force," through any part of the test as shown by the 
curve ? If so, up to what point ? 



40 LABORATORY EXERCISES 

Conclusion : 

(1) State the relation between the tension of a wire 
and its elongation (a) up to the elastic limit, (6) beyond 
the elastic limit. 

(2) Arrange the materials tested in the order of their 
tensile strength, placing the strongest first. 

EXPERIMENT 8 

Relation between Pressure and Depth 

OBJECT. — To find the relation between the depth of a sub- 
merged surface and the pressure upon it. 

Apfaratus. 1 A test tube loaded with shot, upon which 
melted paraffin has been poured, so that the tube will float 
vertically; a paper centimeter scale, attached vertically to the 
inside of the tube with paraffin; weights — 1 to 10 grams if 
a 6" x f " test tube is used and 5 to 20 grams if a 8" x 1" test 
tube is used ; battery jar or hydrometer jar ; cross section paper. 

Introductory : 

When a stick is thrown endwise into water, it springs 
back into the air. When a boat floats in water, there 
must be an upward pressure of the water on it to balance 
its weight. When more heavily loaded, it sinks more 
deeply, but the upward pressure must then also balance its 
weight. 

Experimental : 

A glass tube loaded so that it will remain upright will 
be floated in a jar of water. A scale on the inside of 
the tube will be used to measure changes in depth. This 

1 The method of this experiment was called to our attention by 
Dr. H. C. Cheston of the High School of Commerce, New York City. 



RELATION BETWEEN PRESSURE AND DEPTH 41 



tube should float freely and should not be allowed to 
touch the sides of the jar. The scale readings are 
taken by sighting through 
the jar along the under side 
of the water surface. By add- 
ing small weights as indicated 
in the table below, the level 
of the bottom of the tube 
may be changed. By compar- 
ing the changes in depth and 
the changees in weight pro- 
ducing them, we may find how 
the upward pressure of the water 
(which balances the weight 
of the tube) varies with the 
depth of the surface on which 
it acts. 

Place your observations in a table near the top of the 
left-hand page. 







E 


r 






-^E^y^^G^FiPoP:- 


I-£I-3£?£?£:-£. :: il z -_P£ 


-I^^^^^—r^; 


'TzzEzzE^Erz—T^zF. 


-,=^-s=sz^zszs 


r^zjnr-inzr - — _n_- 


—^-.^--^z^-^-s-^^zs 


rzErzTEEE^zEEE 1 ^ 


zszj^rzr~rzszs:szsz 





i_-_r-zz_-z_-zi.--z_-z_ 


ErErErZi^rEzEzEiEr 


















£EEE3E7EE€EEEE>: 


^ 


T 


Tzsrzj^zsi^zszjrzszs 




EI^^^3-I-3EE^^|feE?EzEEz7^^Er^ 






































" 



Fig. 11. 



Number of 
Observation 

1 

2 
3 
4 
5 
6 



Observations 

Weight 



Loaded tube alone .... 
Loaded tube alone + 2 grams 
Loaded tube alone + 4 grams 
Loaded tube alone + 6 grams 
Loaded tube alone + 8 grams 
Loaded tube alone + 10 grams 



Scale 
Reading 

cm. 
cm. 
cm. 
cm. 
cm. 
cm. 



Make a drawing from your apparatus and write a simple 
description of the method of the experiment. 

Make the following tabulations at the top of the right- 
hand page: 



42 LABORATORY EXERCISES 

Calculated Results 



Numbers 

1 — 2 
1 — 3 
1 — 1 
1 — 5 
1 — 6 



Change of 


Change of 


Pressure 


Depth 


grams . 


cm. 


grams 


, . cm. 


grams 


cm. 


grams . 


cm. 


grams . 


. . cm. 



Curve on Cross Section Paper. — The readings of change 
of pressure and change of depth should be plotted on 
cross section paper, depths on the perpendicular axis and 
pressures on the horizontal axis. Use a scale of 5 small 
spaces to 1 gram, and 2 small spaces to 1 mm. If the 
resulting graph is a straight line, we may conclude that 
twice the depth was caused by twice the pressure and so 
on, or that the pressure is directly proportional to the 
depth. Paste the cross section paper by one edge in the 
note-book. 

Discussion : 

At each observation in the experiment, what relation 
must exist between the total weight of the floating tube 
and the upward pressure of the water? Why is it not 
necessary to consider any sidewise pressures that may be 
exerted on the tube ? 

Conclusion : 

What is the relation between the pressure on a sub- 
merged surface and the distance of that surface below the 
surface of the liquid? 



ARCHIMEDES' PRINCIPLE 43 

EXPERIMENT 9 

Archimedes' Principle 

OBJECT. To determine the relation between the loss of weight 
of a sinking solid and the weight of a liquid displaced by it. 

Apparatus. Lump of coal with thread, or copper wire #22 at- 
tached ; overflow can ; catch bucket or beaker with wire loop for 
suspension ; spring balance (250 g.), or beam balance ; battery jar. 

Introductory : 

It is much easier to lift the anchor of a boat when the 
anchor is in the water than when it is out of the water. 
The displaced water supports part of the weight of the 
anchor, and so makes it seem lighter, because the upward 
pressure of the water on the bottom of the anchor is 
greater than the downward pressure on the top. The 
anchor displaces a volume of water its own size. We wish 
to compare the loss of weight of a body submerged in a 
liquid with the weight of the liquid displaced by it. 
This was first done by Archimedes, and the relation found 
is called Archimedes' Principle. 

Experimental : 

Use a piece of coal for the solid. By weighing it 
in air, with a spring balance, and then when immersed in 
water in a jar, the loss in weight of the lump can be found. 

When a can with a spout, called an overflow can, is filled 
and placed on a level table, the water will run out to the 
level of the spout. By placing a weighed beaker under 
the spout and carefully lowering the coal into the can, 
the water which overflows may be caught and weighed. 
Comparing the weight of this displaced water with the 
loss of weight of the coal, will give the relation sought. 



44 



LABORATORY EXERCISES 



Record the following readings in tabular form near the 
top of the left-hand page : 



Observations 

Weight of coal in air 

Weight of coal in ivater . . . ... 

Weight of catch bucket 

Weight of catch bucket + displaced ivater 



9- 

g< 
g- 
g- 



Briefly describe what you did, illustrating each step 
with a drawing from your apparatus, similar to Fig. 12 
(A, B, and 6 7 ). 



A 



T 



B 




T 





Fig. 12. 

Calculated Results 



Loss of weight of coal in water . 
Weight of an equal volume of ivater 



g- 

9- 



Conclusion : 

State the relation between the loss of weight of a sink- 
ing body and the weight of a liquid displaced by it. 



LAW OF FLOTATION 



45 



EXPERIMENT 10 



Law of Flotation 

OBJECT. — To determine the relation between the weight of a 
floating body and the weight of a liquid displaced by it. 

Apparatus. Block loaded to float upright on water ; overflow 
can ; catch bucket or beaker with wire loop for suspension ; 
spring or beam balance. 

Introductory : 

The cork float on a fishline exerts no pull on the line. 
The weight of an ocean liner is supported by the upward 
push of the water. A boat is said to have a certain num- 
ber of tons displacement, 
depending upon its size and 
weight. What is the rela- 
tion between this number 
of tons of water displaced 
and the weight of the boat ? 

Experimental : 

A method similar to that 
used in Experiment 9 will 
give us the relation between 
the weight of the wooden 
block and the weight of the 
liquid displaced by it. Place the table of observations 
near the top of the left-hand page. 



A 



T 




A 



B 



Fig. 13. 



Observations 

Weight of block 

Weight of catch bucket, empty . 

Weight of catch bucket + displaced water 



9- 



46 LABORATORY EXERCISES 

Write a simple description of the steps in the experi- 
ment, illustrating each with a drawing from your apparatus. 

Place the table of calculated results at the top of the 
right-hand page. 

Calculated Results 

Weight of water displaced by floating body . „ g. 

. , . [floating body .... g. 

Comparison of weights \ ,. , , 

r * * I displaced water ... g. 

Conclusion : 

The weight of a floating body and the weight of the 
liquid displaced by it are . 



EXPERIMENT 10 (Alternative) 

Law of Flotation 

OBJECT. To determine the relation between the weight of a 
floating body and the weight of the liquid displaced by it. 

Apparatus. A wooden bar 20 cm. long and 1 cm. square 
with metric scale attached and loaded so as to be almost sub- 
merged when floating upright in water; 1 hydrometer jar or 
battery jar ; platform balance ; metric weights. 

Introductory : 

The cork float on a fishline exerts no pull on the line. 
The weight of an ocean liner is supported by the upward 
push of the water. A boat is said to have a certain num- 
ber of tons displacement, depending upon its size and 

1 The ordinary wooden hydrometer can he made available by drilling 
a hole in the lower end, adding lead shot, and closing with a cork plug. 
The weight of the bar should be so adjusted that the bar will float almost 
submerged. Finally put a light coat of paraffin over the end which was 
opened. 



LAW OF FLOTATION 



47 



weight. What is the relation between this number of 
tons of water displaced and the weight of the boat ? 

Experimental: 

The wooden bar is to be weighed and then floated in 
the water of jar so as to note the depth to which 
it is submerged. The metric scale on the bar 
gives the length of the column of water dis- 
placed and, like the bar the column of displaced 
water, is 1 centimeter square. Therefore the 
reading on the metric scale is numerically equal 
to the number of cubic centimeters of displaced 
water. Since a cubic centimeter of water at 
ordinary temperatures weighs approximately a 
gram, the weight of the displaced water can eas- 
ily be found. A comparison of the weight of the 
floating bar and the weight of the displaced Fig. 14. 
water will bring out the principle of flotation. 



^-" . "X 



Observations 



Weight of bar 

Length of column of displaced water 



9- 
cm, 



Make a drawing of the floating bar from your apparatus 
and write a simple description of the experimental method. 

Calculated Results 



Volume of water displaced by floating body 

Weight of water displaced by floating body 

_. . _ . . f floating body 

Comparison of iveiqhts < 7 . 7 7 

1 * a [ displaced water . 

Conclusion : 



cm, 

9- 
9- 
9- 



The weight of a floating body and the weight of the 
liquid displaced by it are . 



48 



LABORATORY EXERCISES 



EXPERIMENT 11 

Specific Gravity of Solids 

OBJECT. To find the specific gravity of various solids. 

Apparatus. Spring balance, or beam balance arranged for 
weighing in water ; battery jar ; pieces of coal, glass, and marble, 
or other solids desired. 

Introductory : 

Lead is a very heavy metal. While a pailful of water 
weighs only about 20 pounds, the weight in pieces of lead 
that would just fill the pail would be about 225 pounds. 
Lead weighs about 11.2 times as much as the same volume 

of water. We say that 



A 



T 




T 



r> the " specific gravity " 

^P\^ of lead is 11.2 times. 

The specific gravity of 
a substance is the num- 
ber of times a piece of 
the substance is as 
heavy as the same vol- 
ume of water. 

Experimental : 

It will be necessary 
to get the weight of a 
_ lump of coal and the 
Fig. is. weight of the same vol- 

ume of water. The 
weight of the coal can be found directly with a spring 
balance, and Archimedes' Principle will help us in getting 
the weight of an equal volume of water. If the coal is 
weighed while immersed in water, it will weigh less than 




SPECIFIC GRAVITY OF SOLIDS 



49 



in air by an amount equal to the weight of water having 
the same size (volume) as the coal. The specific gravity 
of the other solids furnished may be found in the same 
way. 

Record the weighings in tabular form near the top of 
the left-hand page. 

Observations 



Weight of body in air . 
Weight of body in water 



Coal 



Marble 



Glass 



Then make drawings from your apparatus and write a 
simple description of how the experiment was done. 

Place the table of calculated results at the top of the 
right-hand page. 

Calculated Results 



Weight of water size of solid 
Weight of solid .... 
Specific gravity of solid 



Coal 



Marble 



Glass 



Conclusion : 

The specific gravity of coal is times; the specific 

gravity of marble is times; the specific gravity of 

glass is times. 



50 



LABORATORY EXERCISES 



EXPERIMENT 12 

Specific Gravity of a Liquid 

(Bottle Method) 

OBJECT. To obtain the specific gravity of a solution of copper 
sulphate with a specific gravity bottle. 

Apparatus. Specific gravity bottle ; spring balance (250 g.) 
with scale pan, or beam balance ; bottle or jar of copper sulphate 
solution provided with a siphon delivery tube, ending with rubber 
connection, pinchcock, and glass jet tube (Fig. 17). 

Material. Water; saturated solution of copper sulphate; 1 small 
cloths for wiping. 



Introductory : 

If we find the weight of a 
gallon of water and of a gallon 
of alcohol, we can directly deter- 
mine the specific gravity of the 
alcohol by finding how many 
times it is as heavy as water. 
This is a general 
method for finding 
the specific gravity 
of any liquid. 




/ 








~-^^^^~^£^€-^rs : 




-I]rE>iL- : Cr^IHIHI-IE-IK?^-F£ : - 




. 








[HrEf—ir^ £?{=£?£?£? I 


: r-~ 


'zrz^--~ - -—-—-'■ : 


-_-. 


IHr^^iFiE^JEF^ 


£z 


--=— — — — - — — - 


\zrz—^=^=r^=r^=z. t=_-=lt: 



- c 



1 



Fig. 16. 



Experimental : 

We use small spe- 
cific gravity bottles 



Fig. 17. Jar and siphon for 
solution. 



having perforated glass stoppers, as in this way we can 

1 A hot saturated solution should be made and allowed to cool, or a 
cheesecloth bag full of copper sulphate crystals should be suspended in 
the top of a jar of water and allowed to stand at least twenty-four hours, 
or until no more copper sulphate will dissolve. 



SPECIFIC GRAVITY OF A LIQUID 51 

obtain very exactly equal volumes of the two liquids. 
The weight of the specific gravity bottle must first be 
found. Then it is to be weighed full of water and next 
full of copper sulphate solution. By comparing the weight 
of the copper sulphate solution filling the bottle with the 
weight of the water filling the same space, the specific 
gravity of the copper sulphate solution may be found. 

CAUTION. Using the wiping cloths if necessary, see that the 
bottle is dry on the outside before weighing and avoid handling it 
except by the neck, for the heat of the hand is likely to drive out 
some of the liquid through the stopper, after it has been fitted. After 
the water weighed has been emptied out, rinse the bottle with a little 
of the sulphate solution. 

Record the weighings in tabular form near the top of 
the left-hand page. 

Observations 

Weight of scale pan and empty bottle .... g. 
Weight of pan and bottle filled with water . . g. 
Weight of pan and bottle filled with copper sul- 
phate solution ' . g. 

Make drawings from your apparatus and write a short 
description of how the experiment was done. 

Place the table of calculated results at the top of the 
right-hand page. 

Calculated Results 

Weight of water filling bottle ...... g. . 

Weight of copper sulphate solution filling bottle . g. 

Specific gravity of copper sulphate solution . . times 

Conclusion : 

The specific gravity of copper sulphate solution is 

times. 



52 LABORATORY EXERCISES 

EXPERIMENT 13 

Specific Gravity of a Liquid 

(Hydrometer Method) 

OBJECT. To find the specific gravity of a copper sulphate solu- 
tion by the hydrometer method. 

Apparatus. Hydrometer jars ; square wooden hydrometer 
graduated in millimeters; glass hydrometer for heavy liquids 
(1 to 2). 

Material. Water ; saturated solution of copper sulphate as 
in Experiment 12. 

Introductory: 

A boat, passing from fresh water into the ocean, rises 
a little, as the boat displaces its own weight in each 
case, and the salt water, being more dense, has less volume 
for the same weight. An electric light bulb in concen- 
trated sulphuric acid floated with 100 c.c. of its volume 
submerged ; in alcohol, which is half as dense as sulphuric 
acid, the same bulb would sink until 200 c.c. were sub- 
merged. We see, then, that the greater the specific gravity 
of a liquid the less portion of a given floating body will be 
submerged in it. More exactly, the volumes of a floating 
body submerged in two liquids are inversely proportional 
to the specific gravities of the two liquids. 

Experimental : 

(a) A graduated float used for obtaining the specific 
gravity of liquids is called an hydrometer. The hydrom- 
eter to be used is a loaded stick 1 cm. square and graduated 
in centimeters and tenths. If we now immerse this in 
water (Fig. 18) and record the depth to which it sinks, 
and then do the same with a copper sulphate solution 



SPECIFIC GRAVITY OF A LIQUID 



53 



(Fig. 19), the hydrometer will sink deeper in the less 
dense liquid. The volume of each liquid displaced may 
be measured by the depth of the submerged part of the 
hydrometer, since each centimeter of length means 1 c.c. 
of volume. If, then, we divide the length submerged in 
in water by the length submerged in copper sulphate, we 
shall obtain the specific gravity of the copper sulphate 
solution. 






^: -•-•■--■■ - .^ 

Fig. 18. 



Fig. 19. 



Fig. 20. 



(5) Direct-reading hydrometers are made of glass tubes 
loaded so as to float upright and provided with a scale 
which gives the specific gravity directly (Fig. 20). After 
completing calculations on part (a), ask the instructor 
for such a hydrometer, and with it find the specific gravity 
of your solution, as a check on your results. Record the 
observations in tabular form near the top of the left-hand 
page. 

Observations 



Heading of bar in tvater 

Heading of bar in copper sulphate solution 
Reading of glass hydrometer in copper sulphate 
solution 



cm, 
cm, 



54 LABORATORY EXERCISES 

Make drawings from your apparatus showing the posi- 
tion of the wooden hydrometer in the two liquids and 
the position of the glass hydrometer in the copper sulphate 
solution. Accompany these drawings with a short de- 
scription of the method of work. 

Calculated Result 

Specific gravity of copper sulphate solution 

as determined by wooden hydrometer . . times 

Discussion : 

Explain why the volume of water displaced was divided 
by the volume of copper sulphate solution displaced. 

Conclusion : 

The specific gravity of the copper sulphate solution 

by this method (wooden hydrometer) is times 

by the bottle method (Experiment 12) is times 

by the direct reading of the glass hydrom- 
eter is times 



SPECIFIC GRAVITY OF A LIQUID 55 

EXPERIMENT 14 

Specific Gravity of a Liquid 

(Hare's Method) 

OBJECT. To find the specific gravity of alcohol and of a salt 
solution by Hare's method. 

Apparatus. Two 90 cm. lengths of \" glass tubing ; lead or 
glass T-tube, or Y-tube ; 2 rubber connections ; black rubber 
tubing of length convenient for suction ; screw compressor ; ring 
stand and clamp for supporting T-tube or Y-tube ; 2 tumblers 
(preferably of thin glass and with nearly vertical sides), or 2 
beakers. 

Material. Distilled water, if available ; saturated solution of 
common salt, and grain alcohol in stock bottles provided with 
siphon tubes about ^" bore. 

Introductory : 

The simple barometer is nothing more than a long tube, 
closed at one end and filled with mercury, which is then 
inverted in a dish of mercury. A mercury column about 
76 centimeters in length remains standing in the tube. 
This column is held up by the pressure of the atmosphere. 
It has also been determined experimentally that the 
pressure of the air supports a much longer column of 
water — approximately 34 feet. We know that mercury, 
volume for volume, is much heavier than water, or, as we 
say, has a greater specific gravity. The fact that the 
atmosphere holds up columns of liquid whose length varies 
with the particular liquid taken, has been utilized in an 
ingenious method for determining the specific gravity of 
liquids. 



56 



LABORATORY EXERCISES 




Experimental : 

The apparatus (Fig. 21) consists of two long parallel 
tubes with their lower ends dipping into tumblers of 

liquids. The upper end of each 
is joined by a rubber connection 
to an arm of a T-tube. To the 
center tube of the T is attached a 
rubber tube to be used for suc- 
tion, which can be closed by a 
screw compressor. 

(a) Half fill one tumbler with 
water and the other with a sat- 
urated solution of salt. 

With the rubber tubing open, 
compare the water levels inside 
and outside the long tube. Ac- 
count for this condition of levels. 
Is it also true for the levels of the 
salt solution ? 

Suck out a little air through 
the rubber tube, noting the be- 
havior of the liquids. What pres- 
sure causes the liquids to rise in the 
tubes ? 

Again remove air by suction 
until the water column is pushed 
up nearly to the top of its tube. 
Pinch the rubber tube tightly and 
close the screw compressor. Note 
the relative height of the two liq- 
uids. The pressure on the upper surfaces of the two 
liquids is the same. How does this pressure compare with 
the outside air pressure ? What pressure forced the liquids 




Fig, 21 



SPECIFIC GRAVITY OF A LIQUID 57 

up into the tubes ? How does this pressure compare with the 
downivard pressure of each liquid? Compare, then, the 
downward pressure of the water column with that of the salt 
solution. 

Measure with a meter stick the length of the water 
column above the level of the water in the tumbler. 
Obtain similarly the length of the column of the salt 
solution. Record the measurements in tabular form near 
the top of the left-hand page. 

(S) Open the compressor and allow the liquids to run 
back into their tumblers. Return the salt solution to its 
stock bottle and rinse out the tumbler. Detach the long 
tube used for the salt solution, and, after washing, attach 
it again. 

Put grain alcohol into the empty tumbler and repeat 
the experiment so as to obtain the length of the water 
and the alcohol columns, taking care not to such the alcohol 
up into the mouth. Tabulate the measurements near the 
top of the left-hand page. 

Return the alcohol to its stock bottle. 

Observations 
Part (<x) : 

Length of the water column cm. 

Length of the salt solution column .... cm. 

Part (5) : 

Length of the water column cm. 

Length of the grain alcohol column .... cm. 

Make an outline drawing of the apparatus used, and 
write a simple description of the general method of the 
experiment. 

With the water and the salt solution, the downward 
pressure per square centimeter of each, balances the same 
amount of atmospheric pressure. The two columns must 



58 LABORATORY EXERCISES 

then have the same weight. Being of equal cross section, 
their lengths are proportional to their volumes. But the 
greater the specific gravity of a liquid, the smaller the 
volume for a given weight. Are the relative weights, 
then, directly or inversely proportional to the heights of the 
columns ? With this relation in mind, calculate the spe- 
cific gravity of the salt solution and of the alcohol, relative 
to water. Record the results in tabular form at the top 
of the right-hand page. 

Calculated Results 

Specific gravity of the salt solution . . = times 

Specific gravity of the alcohol .... = times 

Discussion : 

Answer under this heading on the right-hand page the 
italicized questions occurring in the directions. 

Conclusion : 

The specific gravity of the salt solution is times; 

the specific gravity of the alcohol is times. 



EXPERIMENT 14 (Alternative) 

Specific Gravity of Liquids 

(Balancing Columns) 

OBJECT. To find the specific gravity of (a) carbon tetrachloride, 
(b) grain alcohol, by the method of balancing columns in a U-tube. 

Apparatus. 2 Mohr burettes (50 c.c.) connected by a piece 
of thick- walled rubber tubing of sufficient length ; H of mann screw 
compressor ; ring stand ; two burette clamps ; 2 glass funnels, 
2\ n ', or tops of two thistle tubes ; beaker; medicine dropper. 



SPECIFIC GRAVITY OF LIQUIDS 59 

Materials. Mercury ; distilled water if available ; carbon 
tetrachloride ; grain alcohol. (Other liquids, such as glycerine 
kerosene, etc., as the instructor desires.) 

Introductory : 

When mercury fills the lower rounded portion of a U- 
tube, the mercury stands at the same level in the two 
arms, since the downward pressure of the air is the same 
on the two mercury surfaces. 

When a certain volume of water is poured into one arm 
of this same tube, and an equal volume of kerosene into 
the other arm, the mercury level in the water arm is 
lower than that in the kerosene arm. Since the mercury 
is free to move, the given volume of water must press 
down with greater weight on the mercury than does the 
same volume of kerosene. Accordingly, volume for 
volume, the kerosene weighs less than the water. Usually 
the specific gravity is found by calculating the ratio be- 
tween weights of equal volumes. Since this is so, might 
not the inverse ratio between the volumes of equal weights 
give the specific gravity ? 

Experimental : 

As we have seen, equal weights may be measured by 
the downward pressure of liquids. The equal weights 
can be obtained by pouring just enough of each liquid 
into its arm of the U-tube, so as to make the two mercury 
surfaces stand at the same level. All that remains is the 
measurement of the volumes of the two liquids and the 
finding of the ratio, remembering that it is an inverse 
one. 

Clamp the two burettes at about a third of their length 
from their lower ends and in a vertical parallel position 
with the 50-c.c. marks horizontally opposite each other. 



60 



LABORATORY EXERCISES 



Slip the screw compressor over the rubber connecting 
tube and attach the ends of the tube to the burettes. 

Pour mercury through a thistle 
tube top or funnel at the top of one 
burette until the mercury surface 
in each burette stands at the 50-c.c. 
graduation, or some mark a short 
distance above (Fig. 22). Squeeze 
out the air bubbles in the connect- 
ing tube before taking the zero 
reading of the mercury levels. 

(a) Record the zero reading of 
the burettes in the table of obser- 
vations. Then close the screw com- 
pressor on the connecting tube. 

Into the right-hand burette pour 
enough carbon tetrachloride to half 
fill the burette. Add about the same 
volume of water to the other burette. 
Cautiously open the compressor a lit- 
tle, noting whether the tetrachloride 
column is balanced by the water. 
If not, close the compressor, add 
more water, and test again. Con- 
tinue in this manner until the water 
balances the tetrachloride, as shown 
by the mercury remaining at the 
same levels when the compressor is 
opened wide. A medicine dropper 
is convenient for adding the last 
portions of water needed. 
Read and record the top levels of the balancing columns. 
Raise the tetrachloride burette so that the mercury just 
runs into the connecting tube. Over this end of the tube 




Fig. 22. 



SPECIFIC GRAVITY OF LIQUIDS 61 

close the screw compressor and slip off the rubber tube, so 
that the tetrachloride can empty into a beaker placed below 
the burette. Pour the tetrachloride into its stock bottle. 

(5) Rinse out the open burette with a few cubic centi- 
meters of alcohol (or other liquid to be used) and again 
connect the rubber tube. 

Then obtain as in (a) a column of alcohol which 
balances the water column in the left-hand burette. 

Record all readings in a tabular form near the top of the 

left-hand page. 

Observations 
Part (a) : 

Reading of mercury levels . ...... cm. 3 

Reading at top of water column ..... cm. 3 

Reading at top of tetrachloride column . . . cm. 8 

Part (b) : 

Reading of mercury levels cm. 3 

Reading at top of water column . . . . . cm. 3 

Reading at top of alcohol column cm. 3 

Make an outline drawing of your apparatus and de- 
scribe briefly how the experiment was done. 

Place the table of calculated results at the top of the 
right-hand page. The specific gravities are to be calcu- 
lated with reference to water. 

Calculated Results 
Part (a) : 

Volume of the water column cm. 3 

Volume of tetrachloride column cm. 3 

Specific gravity of tetrachloride . . = times 

Part (b) : 

Volume of water column cm. 3 

Volume of alcohol column ....... cm. 3 

Specific gravity of alcohol .... = times 



62 LABORATORY EXERCISES 

Discussion : 

Why is the specific gravity in this experiment the in- 
verse ratio of the volumes of the balancing columns ? 

Conclusion : 

The specific gravity of carbon tetrachloride is 

times. The specific gravity of alcohol is times. 



EXPERIMENT 15 

Density of Air 

OBJECT. To determine the approximate density of air in the 
room. 

Apparatus. Air pump; round-bottom flask (250 c.c.) with a 
tightly fitting 1-hole rubber stopper carrying a glass inlet tube 
with a piece of thick-walled rubber tubing attached; screw 
compressor; beam or horn pan balance weighing to 0.01 gram; 
metric weights ; graduate ; large battery jar, or pail. 

Introductory : 

It is very evident that lead has weight. Even a small 
child knows that a tumbler of water is heavier than the 
empty glass. We know that solids and liquids have 
weight, but does the air which surrounds us have weight? 
If balloons are lighter than air, the air must have weight. 
It would be interesting to find out just how dense air is, 
that is, the number of grams to a cubic centimeter. 

Experimental : 

A flask may be weighed full of air and then the air 
partially pumped out. Then the exhausted flask may be 
weighed. The difference between the two weights is the 
weight of air pumped out of the flask. The volume of 



DENSITY OF AIR 



63 





Fig. 23. 



this air may be found by measuring the water which will 
run into the exhausted flask. With the 
weight and volume of the air known, the 
density (grams per cubic centimeter) may 
be found. 

Make all weighings to the nearest cen- 
tigram. In all weighings of the flask, in- 
clude the rubber stopper with its tubing 
and screw compressor, and any wire sus- 
pension used with the balance. See that 
all joints between rubber and glass are 
tight before exhaustion. Allow at least 
five minutes for the exhaustion of the 

flask, and be sure 
the screw compres- 
sor is tightly closed 
before the removal 
of the rubber tube from the pump. 
Immerse most of the flask in 
water and open the screw com- 
pressor a little at a time under 
water. As soon as no more water 
will run in, move the flask so that 
the level of the water on the in- 
side is the same as that on the 
outside (Fig. 24). 

Pinch the rubber tube with 
the compressor so as to close it, 
and remove the flask from the 
water. Set it in a secure upright 
position on the table. Open the 
compressor so as to allow the water 
in the small tube to run down into the flask and then re- 
move the stopper and its connections. 



Fig. 24. 



64 LABORATORY EXERCISES 

Measure with a graduate the volume of water in the 
flask. 

Record the measurements in tabular form near the top 
of the left-hand page. . 

Observations 

Weight of flask filled with air g. 

Weight of flash, air exhausted g. 

Volume of air exhausted cm. s 

Record, if so directed by the instructor, the temperature 
of the room and the barometric pressure. 

Briefly describe the steps in the experiment, illustrat- 
ing with drawings from your apparatus. 

Place the table of calculated results at the top of the 
right-hand page. 

Calculated Results 

Weight of air exhausted g. 

Volume of air exhausted cm. 3 

Density of air grams 

cm. s 
Discussion : 

After the water had run into the flask, the water levels 
were made the same, so that any air not pumped out of 
the flask would be at the same pressure as the air in the 
room. What is the necessity for this precaution ? Would 
the results obtained for this experiment be exactly the 
same on different days ? Give reasons for your answer. 

Conclusion : 

The density of the air in the laboratory at the existing 
conditions was grams per cubic centimeter. 



DENSITY OF AIR 65 

EXPERIMENT 15 (Alternative) 

Density of Air 

OBJECT. To determine the approximate density of air in the 
room. 

Apparatus. Incandescent lamp bulb; Bunsen burner ; blow- 
pipe ; small battery jar ; small funnel and graduate ; horn pan 
balance weighing to 0.01 gram or better ; metric weights ; small 
squares of adhesive plaster. 1 

Introductory : 

It is very evident that lead has weight. Even a small 
child knows that a tumbler of water is heavier than the 
empty glass. We know that solids and liquids have 
weight, but does the air which surrounds us have weight ? 
If balloons are lighter than air, then air must have weight. 
It would be interesting to ascertain just how dense air is, 
that is, the number of grams to a cubic centimeter. 

Experimental : 

The bulb of an incandescent lamp is empty save for 
the filament and a very slight trace of gas which was not 
exhausted. The bulb then can be weighed empty. By 
making a small hole, the air will rush in and fill the bulb. 
Another weighing gives the weight of the bulb filled with 
air. The difference between the two weighings is the 
weight of the air in the bulb. The volume of this air 
may be found by filling the bulb with water and then 
measuring the water with a graduate. With the weight 

1 Note to Instructor, If the supply of burnt-out bulbs is limited, the 
experiment may be done in small squads, each student making the 
weighings and measurements for himself. In small classes the instructor 
may prefer to make the first air hole with the blowpipe. 



66 



LABORATORY EXERCISES 




Fig. 25, 



and volume of the air known, the number of grams per 
cubic centimeter can be calculated. 

Filling the Bulb with Air. — Use the tiny point of a 

blowpipe flame, but approach the portion to be heated 
very gradually with the flame so as to 
avoid the sudden cracking and collapsing 
of the bulb. Heat a small area near the 
top of the bulb where the diameter is 
greatest (Fig. 25). As the glass softens 
at the tip of the blowpipe flame, the pres- 
sure of the outside air will make a hole. 
Any bits of glass which may be chipped 
off will tend to be drawn inward so that 

there will be no loss of weight due to the glass. Only a 

tiny hole is needed to admit the air. 

Filling the Bulb with Hater. — After the bulb has 

been weighed full of air, heat it with the tip of a blow- 
pipe flame so as to make a little hole in the glass an inch 

or so from the base of the lamp. 

When the heated glass is cool, immerse the bulb upright 

in the water of a battery jar so as to leave the first air hole 

made just above the surface of the water 

(Fig. 26). When the bulb is nearly full, 

incline the bulb, so that the rest of the 

space can fill with water. 

Then take the small square of adhesive 

plaster and stick over the lower hole, 

holding it in position for a couple of 

minutes with the finger. Now cover the 

upper air hole with the finger and remove 

the bulb from the water. Holding the 

bulb nearly upright over a funnel sup- 
ported in a graduate, pierce through the adhesive plaster 

just over the lower air hole. When the finger over the 




Fig. 26. 



DENSITY OF AIR 67 

upper air hole is removed, the water will run down into 
the funnel. Remember that the outward flow may be 
stopped at any time by closing the upper hole with the 
finger. 

Record the measurements in tabular form near the top 
of the left-hand page. 

Observations 

Weight of incandescent bulb empty .... g. 

Weight of bulb filed with air g. 

Volume of air filing bulb . . . . . . cm. s 

Record, if so directed, the temperature of the air in the 
room and the barometric pressure. 

Describe briefly the steps in the experiment and illus- 
trate with drawings from your apparatus. 

Place the table of calculated results at the top of the 
right-hand page. 

Calculated Results 

Weight of air filling bulb g. 

Volume of air filling bulb cm. s 

Approximate density of air . . . . , ?- 



cm. 3 



Conclusion 



The approximate density of air in room at existing con- 
ditions was grams per cubic centimeter. 



68 LABORATORY EXERCISES 

EXPERIMENT 16 

Boyle's Law 

OBJECT. To find how the volume of a gas varies with the pres- 
sure exerted upon it. 

Apparatus. Barometer ; Boyle's Law apparatus as furnished 
by dealers in scientific instruments. The two forms recommended 
are : ( 1 ) the apparatus with the closed tube ending in glass stop- 
cock, and the open tube connected with the closed tube by heavy- 
walled tubing;. (2) the apparatus with both tubes dipping into a 
mercury reservoir, the closed tube sealed at the upper end, and 
a small bicycle pump to produce pressure in reservoir, so as to 
make mercury rise in the two tubes. 1 

Material. Mercury, if not supplied with the apparatus. 

Introductory : 

A bicycle pump takes in air and makes it occupy a much 
smaller space. We know that the air in the inflated tube 
is under much greater pressure than before. Oxygen is 
sold in steel cylinders filled under pressure. When the 
valve is opened, many jars of oxygen may be obtained from 
one tank for experiments in the chemical laboratory. 
The total volume of the, jars filled is far greater than that 
of the cylinder, for the oxygen is under much less pressure 
in the jars than in the steel tank. The two instances of 

1 Note to Instructor. The directions for this experiment have been 
written so that either of the two forms of apparatus may be used. Both 
forms are on hand in many schools. A good type of the first apparatus 
maybe obtained from the C. H. Stoelting Co., Chicago (list number 1151); 
the second form with an improved mercury reservoir is made by the 
L. E. Knott Apparatus Co., Boston (list number 41-105). 

The authors regard the J-tube form as very desirable for demonstration 
purposes, but less fit for the laboratory experiment, as most students are 
unable to handle it without spilling the mercury required. 



BOYLE'S LAW 69 

the inflated tire and the filling of jars with oxygen show 
that there is some relation between the volume of the gas 
and the pressure exerted on it. Whether or not there 
is any regularity in this relation, may be ascertained 
by experiment. 

Experimental : 

Specific directions for handling the apparatus will be 
given by the instructor. 

The volume of air used is that inclosed above the 
mercury in the closed tube. The mercury in the open 
tube is used for varying the pressure upon the inclosed 
air. When the mercury levels are the same in the two 
tubes, the inclosed air is under atmospheric pressure. 
When the mercury level is higher in the open tube, 
then the inclosed air is under more than atmospheric 
pressure, for a column of mercury equal in height to the 
difference in levels is adding its pressure to the atmospheric 
pressure. A lower level in the open tube means a pressure 
less than the atmospheric. 

The pressure is expressed in centimeters of mercury. 
If the bore of the closed tube is of uniform diameter, the 
length of the inclosed air column may be taken as the 
measure of its volume and recorded in centimeters. 

Make a number of readings, as directed by the in- 
structor. The difference of the mercury levels in the 
open tube between successive readings, should be about 
10 cm. One reading should be made with the mercury at 
the same level in the two tubes. 

As soon as the readings are made, record them in tabu- 
lar form at the top of the left-hand page. 

Write a simple description of the method of using the 
apparatus and make an outline drawing of it, showing the 
essential parts. 



70 



LABORATORY EXERCISES 



Observations 



Number of 


Column of Inclosed Air 


Mercury Level 


[Beading 


Top 


Bottom 


Open Tube 


1 
9 

etc. 


cm. 
cm. 


cm. 
cm. 


cm. 
cm. 



Barometric pressure at on was 

x (thin') (date) 



mm. 



cm. 



Place the calculated results in tabular form at the top 
of the right-hand page. The difference in the mercury 
levels can be found from the quantities in the last two 
columns of the table of observations. 

The pressure of the inclosed air is atmospheric pressure 
plies or minus (as the case may be) the difference of 
mercury levels. In recording the product of the pressure 
by the volume, omit the decimal fractions. 

Calculated Results 



Number of 
Reading 


Difference 
in Levels 


Pressure of 
Inclosed Air 


Volume of 

In( losed Air 


Press ure X 
Volume 


1 

2 

etc. 


cm. 
cm. 


cm. 

cm. 


cm. 3 
cm. 3 





Discussion : 

Is the product of the pressure and the volume approxi- 
mately constant ? Why should the temperature of the 
inclosed air not change while the readings are being made? 
Would a variation in the barometric pressure during the 
experiment affect the result ? 

Conclusion : 

Complete the following statement : 

At a constant temperature, the volume of a given mass 
of gas varies -• as the pressure sustained by it. 



MEASUREMENT OF GAS PRESSURE 71 

EXPERIMENT 17 

Measurement of Gas Pressure 

OBJECT. To measure the pressure of the laboratory gas supply. 

Apparatus. Water manometer, consisting of a U-tube (8") 
with one arm carrying a tightly fitting 1-hole rubber stopper with 
glass elbow tube ; l block with slot or groove for supporting U-tube ; 
foot rule or a metric scale ; rubber tubing for connecting ma- 
nometer with gas cock ; barometer. 

Introductory : 

The bag of a balloon connected with a gas main, fills 
and rounds out as the gas rushes in. One can feel the 
gas pressing out when a stopcock is opened from the gas 
supj)ly in the laboratory. The balloon fills and the gas 
rushes into the room despite the fact that the weight of 
the air is pressing around the bag of the balloon and 
against the opening of the gas cock. This pressure, which 
is effective against the atmospheric pressure, may be de- 
scribed as the effective pressure of the gas supply. How 
much is the effective pressure of the gas delivered to our 
homes and school ? 

Experimental : 

Enough water is added to the U-tube to fill it about 
halfway up, and then the stopper carrying the elbow tube 
is pressed tightly into one arm of the tube. The water 
levels in the two arms are at the same height, since the 
air presses down on both water surfaces equally. 

The elbow tube is connected by a rubber tubing with 

1 Instead of the U-tube, a U-shaped bend of glass tubing with the arms 
about 8 " long, may be used. A Skidmore stand is very convenient for 
supporting the U-tube. 



72 



LABORATORY EXERCISES 



the gas supply. The gas stopcock is slowly turned on 
and the difference in the height of the water levels meas- 
ured. This measurement should be made as soon as the 
rising water level reaches its greatest height. 



Observations 

Atmospheric pressure (barometer reading} 
Difference in height of water levels . 
Time when readings were made . 



in. 
in. 



If the measurements were made in centimeters, change 
them to inches by multiplying by 0.3937. 

Write a simple description 
of the experiment and make 
a drawing showing how your 
apparatus indicated the gas 
s — E T \ pressure. 

The difference of the water 
levels due to the increased 
pressure is independent of the 
cross section of the U-tube, 
therefore we can consider its 
cross section to be 1 square 
inch. A pressure of 14.7 
pounds to the square inch 
holds up a water column 
33.57 feet in length. From 
this equivalent, calculate the 
pressure in pounds per square 
inch of a column of water 
equal in height to the differ- 
ence of levels measured in 
the U-tube. This will give the effective pressure of the gas. 
A pressure of 14.7 pounds to the square inch holds up 




Fig. 27. 



MEASUREMENT OF GAS PRESSURE 73 

a mercury column 30 inches in length. From this rela- 
tion, calculate the pressure in pounds per square inch 
which is equivalent to the observed barometric reading. 

Adding the effective pressure to the atmospheric pres- 
sure gives the total pressure of the gas, that is, the pressure 
per square inch within the gas pipes. 

Record the calculated results in a table at the top of 
the right-hand page. 

Calculated Results 

Effective pressure of gas per sq. in lb. 

Atmospheric pressure per sq. in lb. 

Total pressure of gas per sq. in lb. 

Discussion : 

Why is it not necessary to remove the air in the arm 
of the U-tube connected with the gas supply? What is 
the gas pressure stated to be in your town or city ? What 
does this mean ? 

Conclusion : 

The effective pressure of the gas in the laboratory at 
on , was pound per square inch. The total 

(time) (date) 

pressure per square inch in the gas pipes was pounds. 



74 LABORATORY EXERCISES 

EXPERIMENT 18 

Water Pumps 

OBJECT. To study the parts and the operation of the simple 
lift pump and the force pump. 

Apparatus. Glass models of a lift pump and a force pump ; 
3 feet of glass tubing (*-") with a short piece of rubber tubing 
attached ; battery jar. 

Introductory : 

The ordinary suction or lift pump has been used for over 
two thousand years. Although both the lift pump and 
the force pump are articles of familiar appearance, few 
can give an intelligent explanation of their operation. 
In these cases, as in other apparently simple devices, the 
study of the principles upon which they are based proves 
fascinating. 

Experimental : 

CAUTION. Handle the glass models with great care. Do not 
spill water around the laboratory. 

(a) Place in a jar of water the lower end of a long 
glass tube which has a short rubber tube on the upper 
end. Compare the water levels in the tube and in the 
jar. Account for the relative levels. 

Suck out through the rubber tube most of the air in the 
glass tube, noting the action of the water. Pinch tightly 
the upper end of the rubber tube. Does the water run 
back ? What pressure holds up the column of water in the 
glass tube ? Release the pressure on the rubber tube. 
What happens? Explain. Why is it necessary to remove 
some of the air in a tube if we want water to be pressed up 
in it? 



WATER PUMPS 



75 



Make three simple diagrams which will show 
what was done in this part of the experiment 
and indicate the results. 

(5) The Lift Pump. — Examine a glass model 
of a lift pump, noting the suction tube, the bar- 
rel, the piston, the two valves, and the spout. 
Make an outline drawing, labeling the parts. 
Starting without any water in the pump, im- 
merse the suction tube in a jar of water and 
operate the pump till it is in full action, noting 
the action of the inclosed air, the water, and the 
two valves on each successive stroke. Record 
the observations in tabular form on the left-hand 
page. What is the main thing accomplished by 
the first few strokes of the pump ? 



_. 



Fig. 28. 



Observations on the Lift Pump 



Stroke 


Valve 


Action of Air 


Action of Water 


Action and 
Use of Yalye 


1st Up 


Lower 








1st Up 


Upper 








1st Down 


Lower 








1st Down 


Upper 








2d Up 


Lower 








2d Up 


Upper 








etc. 


etc. 









(e) By a rubber connection attach a long glass tube 
to the suction pipe of the lift pump. Dip the free end of 
the long tube into a jar of water placed on the laboratory 
floor. Can you pump water from the floor? What limits 
the vertical distance through which water can be taken by a 
lift pump even though it were mechanically perfect ? 



76 



LABORATORY EXERCISES 




(d) The Force Pump. — Examine the glass model of a 
force pump, noting its parts. Try its action. 

Make two diagrams showing the action 
of the pump — one for the up stroke, the 
other for the down. Show water levels, 
and use arrows to indicate the direction 
of water flow. 

Will the force pump or the lift pump 
raise water to a higher level ? Why is 
this so ? 

Do not write a description of the work 
done, as the drawings and tabulations 
show this. A few explanatory statements 
may be added if necessary. 



t 



A 



Fig. 29. 



Discussion : 

Under this heading, on the right-hand 
page, answer the italicized questions in the 
experimental directions. 
Is the action of these pumps due to pressure or to " suc- 
tion." Which type of pump is a bicycle pump? Explain. 
Why is a little water sometimes poured in at the top 
of a pump just before working the handle? (Class Dis- 
cussion.) 



THE PRINCIPLE OF MOMENTS 77 

EXPERIMENT 19 

The Principle of Moments 

OBJECT. When three parallel forces are in equilibrium, to com- 
pare (a) the forces in one direction with the force in the opposite 
direction; (&) the clockwise moments with the counterclockwise 
moments. 

Apparatus. Meter stick ; loops of strong cord ; 3 spring balances 
(2000 grams), with hooks for suspending them, or clamps for 
fastening the balances to the edge of the table top (Fig. 35 ). 1 

Introductory : 

When a team of horses is drawing a wagon, their com- 
bined force forward is exerted to overcome the resistance 
of the wagon pulling backward. When two boys carry a 
heavy weight suspended from a stick, the boys pull up- 
ward and the weight pulls downward. If the boys have 
not equal strength, the weight will be shifted toward one 
of the boys. Which one? 

In each of these cases, we have three forces parallel to 
each other, two in one direction and one in the other. 
These forces are in equilibrium when the stick is balanced. 
If one boy should lift more than he had been lifting, the 
stick would turn toward him. The turning effect of a 
force is called the moment of the force. 

We can imitate either of these cases by attaching three 
spring balances to a meter stick, so that two pull in one 
direction and one in the other. We can then compare 
(a) the pull of the two forces in one direction with that 

1 This experiment can also be conveniently done by using two balances 
suspended vertically with a weight between, supported by a loop on the 
meter stick so that the weight may be moved to positions of equilibrium. 
If this modification is made, allowances must be made for the pull on the 
balances due to the weight of the meter stick. 



78 



LABORATORY EXERCISES 



of the single force in the other, and compare (J) the turn- 
ing effect or moment of the force at one end with that 
of the force at the other end of the stick. 

Experimental : 

The apparatus will be arranged as shown in the diagram 
(Fig. 30). The amount of each force may be read on the 
balance. First each outside cord should be placed 10 cm. 

from its end of the meter 
stick and the third cord 
in the center. See that 
all cords are parallel. 
The highest reading on 
any balance should not 
be more than 1600 grams. 
When all is adjusted, the 
reading of each balance 
and the position of each 
string on the meter stick 
should be recorded (I). 
One end balance may then be shifted so that it is half 
as far from the center as the other. After adjustment, 
readings should again be taken (II). The total force in 
one direction may then be compared with the total force 
in the other, as indicated in the table for the right-hand 
page. The moment of a force is found by multiplying 
the force by its lever arm. The lever arm is the perpen- 
dicular distance from the fulcrum about which the force is 
trying to turn the body, to the force. In this experiment, 
the distance between each of the outer cords and the center 
cord will be the lever arm for the force applied by the 
cord, if the cords are at right angles to the meter stick. 
The moment of each of the end forces around the center 
cord is to be computed. 




Fig. 30. 



THE PRINCIPLE OF MOMENTS 79 

Record the readings in tabular form near the top of the 

left-hand page. 

Observations 

i ii 

Heading of balance A. 

Reading of balance B . 

Heading of balance C . 

Point of application of force A 

Point of application of force B 

Point of application of force 

Make a drawing of your apparatus and write a simple 
description of how it was used. Place the table of calcu- 
lated results at the top of the right-hand page. 

Calculated Results 

i ii 

Combined Force of A and B 

Force of C 

Moment of A about 0. . . . . . 

Moment of B about O _____ 

Discussion : 

Is the moment of A about O clockwise or counter- 
clockwise ? Is the moment of B about clockwise or 
counterclockwise ? 

Conclusion : 

Complete the following with a statement about the 
amount of force in each direction : 

When three parallel forces act on the same body to pro- 
duce equilibrium, then 

Complete the following by comparing with the moment 
of the third force around the second, both as to magnitude 
and direction : 

When three parallel forces act on the same body to 
produce equilibrium, the moment of one of them about 
the second is 



80 



LABORATORY EXERCISES 



EXPERIMENT 20 

The Lever Arm of a Force 

OBJECT. To determine the lever arms of non-parallel forces. 

Apparatus. Meter stick, with a hole on the center division 
near one edge, drilled slightly larger than the shank of a J" screw 
eye; short piece of board about }" stock; screw eye, T " ; fish 
line; four clamps; half meter stick; draughtsman's triangle, 
90°, 60°, and 30.° 

Introductory : 

In using such a lever as a crowbar, pump handle, or 
hammer, it is seldom that the forces exerted on and by the 
lever are parallel to one another. Under such circum- 
stances, it would be desirable to know whether the lever 
arm is to be measured along the lever or at right angles to 
the applied force. 





7 



Fig. 31 




THE LEVER ARM OF A FORCE 81 

Experimental : 

The meter stick is to be attached by the screw eye to a 
short board held firmly by two clamps to the edge of the 
laboratory table. The 
meter stick must be free xkf 
to rotate around the shank 
of the screw eye as a ful- 
crum. 

The hook of each bal- 
ance is to be attached by a 
loop to the meter stick. 
The other end of each bal- 
ance is to be clamped to Fi 32 
the edge of the table op- 
posite the meter stick. These two balances are to be 
clamped so that they make acute angles with the meter 
stick and, if possible, these angles should be different, as 
shown in Fig. 31. 

Perpendicular distances may be measured by using a 
triangle and a half meter stick, as shown in Fig. 32. 

Make the following readings and record in tabular form 
near the top of the left-hand page of note-book. 

Observations 

Reading of balance A g 

Reading of balance B g 

Point of application of force A . . . . cm 

Point of application of force B . . . ■■* . cm 

Position of fulcrum on meter stick .... cm 

Perpendicular distance, fulcrum to force A . cm 

Perpendicular distance, fulcrum to force B . cm 

Make one drawing showing the arrangement of your 
apparatus and another drawing showing the method of 



82 LABORATORY EXERCISES 

measuring the perpendicular distance of a force from the 
fulcrum. Write a simple description of how the experi- 
ment was done, referring to the drawings. Place the table 
of calculated results at. the top of the right-hand page and 
make all the calculations on that page. 

Calculated Results 

Distance along stick from fulcrum to a . . . cm. 

Distance along stick from fulcrum to b . . . cm. 

Force A x meter stick distance from fulcrum . 
Force B x meter stick distance from fulcrum . 
Force A x perpendicular distance from fulcrum 
Force B x perpendicular distance from fulcrum 

Discussion : 

Which pair of products, in the table above, more nearly 
agrees with the principle of moments? 

Conclusion: 

How should the lever arm of a force always be measured? 



EXPERIMENT 21 

Composition of Several Parallel Forces 

OBJECT. When a number of parallel forces are in equilibrium, 
to compare (a) the forces in one direction with the forces in the 
opposite direction; (b) the clockwise moments with the counter- 
clockwise moments. 

Apparatus. Meter stick ; four or more spring balances 
(2000 g.), with cords and clamps. 



COMPOSITION OF SEVERAL PARALLEL FORCES 83 

Introductory : 

A floor or bridge beam is frequently supported at more 
than two points and has a number of different persons or 
objects exerting their weights on it at various points. It 
is interesting to determine whether the principle of 
moments which has been tested for two forces acting 
about the point of application of a third as a fulcrum, 
will apply to this case also. 

Experimental : 

Four or more spring balances, as the instructor may 
direct, are to be attached by cords to a meter stick, as in 



*850 g 



'lOOOgr 



25.2- 



-20.9- 



kxoog 



-65.4- 



*F 



-12->j 



v750flr 



Scale lcm =500 17 



18000 



Fig. 33. 



the experiment on the Principle of Moments (see Fig. 30, 
page 78). The balances should then be strained and 
clamped in place in such a way as to make all the cords 
parallel, and at right angles to the meter stick. 

The amounts of various forces and their lever arms are 
to be recorded near the top of the left-hand page in the 
form of a diagram like that shown in Fig. 33. Letter 
the forces in order from left to right. 



84 



LABORATORY EXERCISES 



Take for the center of moments some point which is 
not the point of application of any of the forces. The 
line representing each force should be drawn to a scale to 
be designated by the instructor and the exact amount of 
the force should be noted at the right of the line repre- 
senting it. The lever arms are indicated by dimension 
lines as shown. No drawing of the apparatus will be 
necessary. A short description, however, of the experi- 
mental method should be written. 

Place a table like the following at the top of the right- 
hand page and make all calculations on that page: 

Calculated Results 



Clocks mi Moments 


Counterclockwise Moments 


Moment of A 

etc 

Total clockwise moments . 


— - — 


Moment of B 

etc 

Total counterclockwise 
moments ..... 



Sum of forces as A, C, E, etc. 
Sum of forces as B, D, etc. 



Conclusion : 

Fill in the blanks in the following statement so that it 
agrees with your results: 

When a number of parallel forces act on a body, it is 

in equilibrium when the of the forces in one direction 

equals the of the forces in the other direction, and 

the total moments equal the total moments 

about any point taken as fulcrum. 



FOUR FORCES AT RIGHT ANGLES 85 

EXPERIMENT 22 

Four Forces at Right Angles 

OBJECT. When four forces at right angles in one plane produce 
equilibrium, to compare (a) the force in any one direction with the 
force in the opposite direction ; (b) the clockwise moments with the 
counterclockwise moments. 

Apparatus. Composition-of-force board with under side rest- 
ing on four steel balls or marbles ; four pegs ; four spring balances 
(2000 g.) with cords and clamps ; meter stick or other metric ruler. 

Introductory : 

Four boys of different ages might pull on the four sides 
of a piece of burlap so as to stretch it parallel to the top 
of a barrel of vegetables while their father finished the 
heading by putting on a hoop. Each boy probably took 
hold of the burlap at the center of his side, but one or 
more of them soon found it advisable to move his hands 
to one side or the other of the center, so as to prevent the 
burlap from being drawn out of his hands. When the 
burlap was properly stretched, four pulls or forces were 
acting at right angles in one plane. Did the principle of 
moments come to the aid of the smaller boys in the 
family so that they could do their share of the stretching ? 

Experimental : 

The hook of each spring balance is to be attached by a 
cord to a peg on the composition-of-force board. The 
pegs should be arranged so that no two of them will be in 
the same row of holes across the board in either direction. 
The other end of each spring balance is to be securely 
clamped (see Fig. 35 on page 89) so that both the cords 
holding it are parallel to a row of holes (Fig. 34). This 



86 



LABORATORY EXERCISES 



c( 



>e\> 



O O (I O O O O 

o o < o • o o 

o o 4 o o o o 

o o o o o • o 

o o o o o »_ o 

o o o o o 

« O O O O < ' 



-e^K 



>o 



latter figure shows the method of attachment of the bal- 
ances to the board, but not the correct location of the pegs. 
The strain on each balance should be at least 500 grams, 

and the board, which is 
free to move on its roller 
bearings, should be 
brought to rest bv the 
equilibrium of the four 
forces at right angles 
pulling on it. 

The amounts of the va- 
rious forces and their 
lever arms are to be re- 
corded in the form of a 
diagram on the left-hand 
page. Draw, in about 
the middle of this page, a square, 7 centimeters on a side, 
and divide each side into centimeter divisions, and lightly 
rule such cross lines as will locate the positions of the four 
pegs or points of application of the several forces. 

Take for the center of moments some point which is 
not the point of application of any of the forces. To a scale 
designated by the instructor, draw a line representing the 
direction and the exact amount of each force. Indicate 
the amount of each force by figures placed to the right of 
the line representing it. The lever arm of each force is to 
be indicated by a dimension line as in Fig. 33, on page 83. 

Calculated Results 



Fig. 34. 



Clockwise Moments 


Counterclockwise Moments 


Moment of 


Moment of 


etc 


etc 




Total counterclockwise 


Total clockwise moments . 


moments 



PARALLELOGRAM OF FORCES 87 

Unless the instructor so directs, make no drawing of 
the apparatus. A short description of the experimental 
method, however, should be written. 

Place a table, like the one on page 86, at the top of the 
right-hand page and make all calculations on that page. 

Conclusion : 

State, when four forces at right angles in one plane pro- 
duce equilibrium : 

(a) the relation of the force in one direction to the force 
in the opposite direction ; 

(5) relation of the clockwise moments to the counter- 
clockwise moments about any point taken as a 
fulcrum. 



EXPERIMENT 23 

Parallelogram of Forces 

OBJECT. To find the relation between three forces acting on a 
body at a point, in order that they may be in equilibrium. 

Apparatus. 3 spring balances (2000 g.) ; fish line or other 
light, strong cord ; 3 Stone clamps or other means of hold- 
ing balances in place ; 30 cm. ruler. 

Note. — Pencils used in this exercise should be hard, with long, 
sharp points. 

Introductory : 

If two boys were to kick a football, one east and the 
other north, at the same instant, the ball would not go in 
either direction, but would take a course somewhere be- 
tween north and east. The general direction that it would 
take would depend upon which force were greater. To 
prevent the football from moving, it would be necessary 



88 LABORATORY EXERCISES 

to apply a third force which should have the proper direc- 
tion and amount to just neutralize the other two. We 
wish to find the relation between three forces at an angle 
to each other, acting on a body at a point in such a way 
as to keep the body at rest. With the football it would 
be possible for a single force to be substituted for the 
forces applied by the two boys. Such an imaginary force 
is known as a resultant force, and the two forces which it 
replaces are component forces. The single force that 
would keep the ball from moving is called the equilibrant 
force. Our problem is to find (a) how the resultant force 
is related to the component forces in direction and magni- 
tude ; (£) how the resultant force is related to the equili- 
brant force. 

Experimental: 

Connect the three spring balances by three cords that 
meet at a point A. Fasten these balances in place 
by clamping the attached wires. Pull on the third balance 
until the pointer on one of the balances is near the end of 
the scale and then clamp the third balance in place. 

Place the right-hand page of the note-book under the 
cords with the center of the page under the point A. 
Mark two points directly beneath each cord. Remove the 
book and through each pair of points draw a line which 
represents in direction the force. Note and record on the 
diagram, the reading of each balance, calling the balances 
B, C, and D. Measure from A along each line a distance 
to represent the magnitude of the force, using a scale of 
1 cm. to 250 grams. Place at the end of each line an 
arrowhead to show the direction of the force. 

Select one force as the equilibrant and lay off from A 
the resultant equal and opposite to the equilibrant. On 
the two lines representing the components, erect a parallel- 



PARALLELOGRAM OF FORCES 



89 



ogram and draw the diagonal from A. Determine the 
magnitude of the force which this diagonal would repre- 
sent. Compare it with the resultant which you laid off 
and drew. 

Mark on the drawing the lengths of the lines and the 
readings of the balances. No table of results is necessary 



WTSg 




Fig. 35. 

on the left-hand page, but write a simple description of 
the method of the experiment. The drawing has already 
been placed on the right-hand page. 

On the second right-hand page place the table of calcu- 
lated results. 



Calculated Results 



Magnitude of resultant . 
Magnitude represented by diagonal 

Discussion: 






(1) What single force would alone produce the same 
effect as the two forces represented by the sides of the 



90 LABORATORY EXERCISES 

parallelogram? (2) Compare the resultant and the diag- 
onal of the parallelogram in direction and in magnitude. 

Conclusion : 

Three forces are in equilibrium when the of two of 

them is in magnitude and in direction to the . 



EXPERIMENT 24 

Resolution of Forces 

OBJECT. Given the resultant of two forces and one of the forces, 
to find the other force. 

Apparatus. 2 spring balances (2000 g.) ; 500-gram weight ; 
fish line ; upright, with ring for cord and notch for boom ; light 
hard-wood boom, about 25 cm. long, with a brad in the end. 

Introductory : 

When a load is hanging from the boom of a derrick, its 
weight is sustained jointly by the tension of the rope sup- 
porting the end of the boom and the outward thrust of 
the boom. These two forces may then be considered as 
the component forces, whose resultant balances the weight 
of the load. If we know the pull on the cord supporting 
the boom and the weight of the load, we can calculate 
the thrust of the boom outward. 

Experimental : 

(a) The apparatus is to be set up as shown in Fig. 36. 
The boom should be horizontal, and when it has been made so, 
a turn of the cord around the brad in the end of the boom 
will keep it from slipping. When all adjustments have 



RESOLUTION OF FORCES 



91 




Fig. 36. 



been made, hold the note-book with the right-hand page 
against the boom, and indicate the direction of the forces 
by dots under the 
cords and a line 
drawn along the 
top of the boom. 
Place a dot at the 
end of the boom, 
immediately under 
the brad. Leave the 
apparatus undis- 
turbed while per- 
forming the oper- 
ations of part (J). 

(5) Replace the 
note-book on the table. From the dot marking the com- 
mon point of application of the forces, draw lines through 
the dots that were placed under the cords. From the 
common point of application, continue outward some dis- 
tance the line drawn along the boom. Lay off on the 
line representing the tension, a distance corresponding to 
the reading of the balance, using a scale of 100 grams to 
the centimeter. Mark the end of the measured distance 
with an arrowhead, indicating the direction of the force. 
Do the same on the line representing the weight. Mark 
beside each line the exact number of grams represented. 

The weight is the equilibrant of the tension of the 
cord and the outward push or thrust of the boom against 
the cord. Therefore draw a line upward from the point 
of application equal in length to the line representing the 
weight. With this line as a diagonal and the line repre- 
senting the tension as one side, complete a parallelogram 
having a side extending outward from the point of applica- 
tion, as a continuation of the line drawn along the boom. 



92 LABORATORY EXERCISES 

This side will represent the thrust in direction and magni- 
tude. From the length of this side, the outward thrust 
of the boom may be calculated, using the scale employed 
in laying off the other -lines. 

(c) Hook a second spring balance between the cord 
and the boom and pull horizontally until the boom just 
slips out of the notch in the upright. Read the balance 
at this point and record below the drawing on the right- 
hand page : 

Force required to pull out boom .... g. 

Since action and reaction are equal, the inward compo- 
nent of the stretched cord on the boom must equal the out- 
ward thrust of the boom on the cord. 

Make a simple sketch of your apparatus and write a 
brief description referring to the sketch. 

Discussion : 

May the resultant of two forces ever be less than one of 
them ? 

Is a rope that is just strong enough to lift a weight 
vertically, strong enough to lift that weight by means of a 
horizontal boom derrick ? 

Conclusion : 

Given the resultant of two component forces and one of 
the components, state how the other component may be 
found. 



FORCE AT THE CENTER OF GRAVITY 93 
EXPERIMENT 25 

Force at the Center of Gravity of a Body 

OBJECT. To find what is the gravitational force acting at the 
center of gravity of a body. 

Apparatus. Half meter stick loaded at one end; 1 ruler or 
other fulcrum properly supported (see Fig. 37) ; 200-gram weight 
with loop of cord attached; spring balance, or platform balance ; 
metric weights. 

Introductory : 

When we shut a heavy door, we push near the outside 
of the door and not near the hinge. A small boy can 
balance a large boy on a seesaw, by sitting farther out 
on the board. When a body is to be turned about an 
axis, the turning power depends upon how much force is 
exerted and how far from the axis the force is exerted. 
The turning power of a force is called the moment of that 
force and is measured by the product of the force and its 
distance from the axis. The moment of the small boy on 
the seesaw is equal to the moment of the large boy. If 
we know the moment of the large boy and the distance 
of the small bov from the fulcrum, we can calculate what 
the small boy weighs. If both boys get off, the board 
can be balanced so it will not touch at either end. The 
point at which a body must be balanced in order to sup- 
port it is called the center of gravity of the body. 

Experimental : 

The body will be a half meter stick loaded at one end. 
This is first to be balanced over a fulcrum in order to find 

lr The loading may be done by attaching a strip of brass, iron, or 
lead to one end of the half meter stick, at right angles to the stick. 



94 



LABORATORY EXERCISES 



the center of gravity (Fig. 37, A*). Then a 200-gram 
weight will be hung about 10 cm. from the free end of the 
bar and the bar again balanced. 

By measuring the distance of the 200-gram weight from 
the fulcrum and multiplying this distance by the weight 
(200 g.), the moment of the 200-gram weight is obtained. 



so 



vJU 



£ 



D.r 



X? 



B 



~¥~^ 



Fig. 37. 

This moment equals the moment of the force at the center 
of gravity about the fulcrum. Then the force at the 
center of gravity is calculated. 

A second trial should be made with the weight at some 
other point on the stick, as 20 cm. from the end. 

Finally the loaded stick is weighed. 

All observations as soon as made should be recorded in 
tabular form near the top of the left-hand page. 

Observations 
Position of center of gravity of loaded l 2 

SolCrC . . . . . » • . • » 

Position of 200 -g. weight 

Position of fulcrum for equilibrium . 

Weight of loaded stick 



FORCE AT THE CENTER OF GRAVITY 95 

Make drawings showing how your apparatus was used 
and write a simple description of how the experiment was 
done. 

Place the table of calculated results at the top of the 
right-hand page. 

Calculated Results 

i 2 

Distance of weight from fulcrum (Z^) 

Distance of center of gravity from 

fulcrum (Z> 2 ) • • 

Moment of weight about fulcrum 

(200 xDj) 

Moment of force at center of gravity 

Calculated force at center of gravity 



Discussion : 

Define moment of force. Explain the calculation of the 
moment of the force at the center of gravity and the cal- 
culation of the amount of this force. 

Conclusion : 

What gravitational force acts at the center of gravity of 
a body. (Compare the last item in both tables.) 



96 LABORATORY EXERCISES 

EXPERIMENT 26 

The Pendulum 

OBJECT. To observe the effect on the number of vibrations of 
a pendulum in one minute of (a) change in mass, (b) change in 
amplitude, (c) change in length. 

Apparatus. A wood and a metal ball each about 1 inch in 
diameter and having a light cord about 125 cm. long attached; 
a support consisting of a split cork in a burette clamp, or a special 
pendulum clamp, so placed that the pendulum may swing freely 
in front of the laboratory table ; metronome or laboratory clock 
with telegraph sounder. 

Note. — Some instructors prefer to have all pendulums in the 
room released ai a given signal and stopped on signal at the end of 
the minute, as confusion is thereby lessened and the student's mind 
is concentrated on the counting. 

Introductory : 

When a clock goes too fast, should the pendulum be 
shortened or lengthened ? We see pendulums made of 
different materials. Does this affect the length of their 
beats ? Does it take a pendulum longer to swing through 
a long arc than a small one ? These are some of the ques- 
tions the experiment will help to answer. By a vibration 
of a pendulum is meant a swing from one end of its arc 
to the other. The period of the pendulum is the time 
that one vibration takes. A seconds pendulum is one that 
swings from one end of the arc to the other in just one 
second ; a half seconds pendulum makes one vibration in 
one half second ; etc. The frequency of the pendulum is 
the number of vibrations per minute. 

Experimental : 

There will be furnished a metal and a wooden ball 
of the same size, attached to a light cord over a meter 



THE PENDULUM 



97 



long. As the suspending cord is very light, we neglect 
its weight and consider the length of the pendulum as 
the distance from the lower edge of the support to the 
center of the suspended ball or "bob." 
For the first test, adjust 



» 



i 



m 



i 



the length of the pendulum 
with the wooden ball to 100 
cm. Count and record the 
number of vibrations made 
in one minute swinging 
through a small arc. Re- 
place with the metal pen- 
dulum and find how many 
vibrations that makes in one ' AM_ 
minute swinging through | 
the same arc. Comparing 
these numbers will show 
whether or not the material 
of the pendulum affects the 
period of vibration. «_> 

Now swing the metal bob Fig. 38. 

through an arc twice as 

great as before, counting the number of vibrations per 
minute. Make the length of the pendulum 50 cm. and 
find the number of vibrations per minute. Repeat with 
lengths of 36 cm. and 25 cm. 

Record all observations in tabular form near the top of 
the left-hand page. 

Observations 

Vibrations per minute, bob wood, length 100 cm., arc 
small 

Vibrations per minute, bob metal, length 100 cm., arc 
small 



98 



LABORATORY EXERCISES 



Vibration* per minute* bob metal, length 100 cm., arc 

large 

Vibrations per minute, bob metal, length 50 cm., arc 

small 

Vibrations per minute, bob metal, length 80 cm., arc 

small 

Vibrations per minute, bob metal, length 25 cm., arc 

S)nall 



Make a drawing of your apparatus and describe briefly 
how the experiment was done. 

Place the table of calculated results at the top of the 
right-hand page and directly below make all the calcula- 
tions called for. 

Calculated Results 



I.i KG i ii 


Xim bi i: <•)■ Vibrations 


PlBIOD 


Squabs of P 


sbiod 


100 cm. 










50 cm. 










36 cm. 










25 cm. 










Conclusioi 


is : 









(a) Does the mass of the pendulum affect the period ? 
(J) Does the amplitude (if comparatively small) affect 
the period ? (e) Is there any simple relation between the 
period and the length ? between the square of the period 
and the length ? 



THE INCLINED PLANE 99 

EXPERIMENT 27 

The Inclined Plane 

OBJECT, (a) To compare the work done in raising a load by 
means of an inclined plane and in raising it vertically; (b)to 
determine the mechanical advantage from the length and height of 
the plane. 

Note. — Only the case when the force is parallel to the plane is con- 
sidered in this experiment. 

Apparatus. Inclined plane properly supported ; car with cord 
attached ; 500-gram weight or other load ; spring balance (2000 g.J. 

Introductory : 

Safe movers roll a safe into a wagon along a sloping 
plank. Does this require less force than to lift the safe 
directly into the wagon ? Is less work done by rolling it 
rip the incline than by lifting it directly ? The plank is 
an example of the use of the inclined plane. We wish to 
answer the above questions by using a car on an inclined 
board in the laboratory. We also wish to find out the 
mechanical advantage of the plane. This is the number 
which is obtained by dividing the resistance by the effort. 
In the inclined plane the mechanical advantage may be 
found also from the dimensions of the plane. We shall 
seek to find what dimensions are used and what division is 
made to obtain the mechanical advantage. 

Experimental : 

An iron car loaded with a 500-gram weight will be used 
and it is to be pulled up an inclined plane by means of a 
cord attached to a spring balance. This balance thus 
measures the force employed to draw the car up the plane. 



100 



LABORATORY EXERCISES 



The combined weight of the car and its load is the weight 
lifted by the use of the plane. It may be found with the 
spring balance. The dimensions of the plane are to be 
measured, as shown in Fig. 39. 

Correction is to be made for some friction. This may 
be eliminated by averaging the reading of the balance 
when the car is moving uniformly up the incline with the 




Fig. 39. 

reading when it is moving uniformly down the plane. 
Decide in each case whether the friction is a help or a hin- 
drance. The work done along the plane is measured by 
the product of the balance reading and the length of the 
plane (to A). The work done in raising the weight an 
equal distance is measured by the product of the weight 
lifted and the height of the plane (at A). 

Record the observations in tabular form near the top of 
the left-hand page. 

Observations 

Weight of car and load g. 

Force required, car ascending g. 

Force required, car descending g. 

Length of plane cm. 

Height of plane .... .' . cm. 



THE INCLINED PLANE 101 

Make a simple sketch of your apparatus and write a 
short description of the method of the experiment. 

Place the table of calculated results at the top of the 
right-hand page. 

Calculated Results 

Average force used c g. 

Work = weight lifted x height of plane . . . g.cm< 

Work = force x length of plane . . . . . g,cm* 

Mechanical advantage = , ^ ..... 

force 

Length of plane 
Height of plane 

Conclusion : 

(a) Compare work done in lifting the load vertically 
from the table to the level of A, with the work done in 
raising it the same vertical distance by rolling it along the 
plane. (6) What relation between the height and length 
of the plane equals the mechanical advantage ? 



102 LABORATORY EXERCISES 



EXPERIMENT 28 

Pulleys 

OBJECT. To study the operation of pulleys and to find their 
mechanical advantage. 

Apparatus. 1 single fixed pulley and 1 double fixed pulley 
with stems for clamping or attaching; single movable pulley; an 
additional movable pulley or a movable double pulley with hooks 
for suspending pan or weights ; support for fixed pulley ; balance 
pan 1 ; metric weights ; spring balance (250 g.) ; meter stick; light, 
strong flexible cord (fish line). 

Introductory : 

The block and tackle is a familiar sight in large cities, 
as it is used for moving pianos and safes in and out of high 
buildings. In the country it is used for pulling stumps 
and handling logs. On the water front, the pulley in 
some form or combination is employed for loading the 
heaviest articles of the cargo. 

Pulleys would not be so widely used unless they 
brought some mechanical gain to their users. The me- 
chanical advantage of a machine may rest in changing 
either the direction or the magnitude of the force applied 
to it. Wherein lies the gain when pulleys are used? 

1 The balance pan for Part (a) is made by first finding with a sensitive 
spring balance the error in indicated weight arising from the use of the 
balance tested in an inverted position. The pan is made from thin sheet 
copper and holes punched in the corners for the fine copper wire used as 
suspension cords. The weight of the pan and its suspension should equal 
the weight error found for the balance. It can be adjusted by filing or 
punching. 



PULLEYS 103 



Experimental 



(a) The Fixed Pulley. A spring balance should be used 
with the hook downward, as the weights of the hook and 
the drawbar were acting on the spring when 
the mark for the zero point was located. In 1 , . H] 
an inverted position the balance will not 
read correctly. To compensate for the error 
arising in this manner, in this experiment, 
the balance pan with its supporting cords has 
been made equal in weight to the drawbar 
and hook. 

The apparatus should be arranged as in 
Fig. 40. A weight is placed in the pan and 
the spring balance is pulled vertically down- 
ward so as to raise the load at a steady rate, Fi 40 
the force or effort necessary being read at 
the same time on the spring balance. Then the balance 
reading is again taken as the load descends at a uniform 
rate. The friction increases the balance reading as the 
load ascends and decreases the reading for the load de- 
scending. An average of the two readings may be con- 
sidered as the force or effort which will just equal the 
resistance to be overcome before the load will move. 

Take readings with 100 grams and 200 grams as the 
loads, and record in tabular form. Note the distance 
through which the load is raised as compared with the 
distance through which the effort moves. Compare the 
load with the effort. What is the only mechanical gain in 
using a single fixed pulley ? 

(V) Single Movable Pulley. The apparatus is arranged 
as in Fig. 41. The total load in this case includes the 
weight of the pan and the weight of the pulley block. 
These are weighed separately and the weights recorded. 



104 



LABORATORY EXERCISES 



Readings are made with the 100-gram and the 200-gram 
weights as in (a). How does the distance through which 
total load (resistance) moves compare 
with the effort distance ? What is the 






Fig. 41. 



Fig. 42. 



Fig. 43. 



mechanical advantage of a tingle movable pulley ? Wliat is 
sacrificed to gain this? 

(<?) Combinations of Pulleys. — A single fixed and a 
single movable pulley are arranged as in Fig. 42. This 
is the arrangement used in the movable scaffolds of 
house painters. Only one set of readings is made — that 
with a load of 200 grams. What additional advantage 
does this combination of pulleys have over the single movable 
pulley ? 

Next, two fixed pulleys (a double pulley) and a single 
movable pulley are combined by the proper adjustment of 
cords. Readings are taken with the 200- and the 500-gram 
weights. The vertical distance through which the load 
moves from the table top is carefully measured as is 
also the distance covered by the effort at the same time. 
Note also the number of cords which support the movable 
block. 

Then & fixed pulley is combined with two movable pulleys 



PULLEYS 



105 



(or a double pullej^) and a similar set of leadings taken 
with weights of 200 and 500 grams. 

Make for (a), (J), and (<?) simple diagrams showing the 
arrangement of the load, the pulleys, and the spring balance. 
Indicate clearly the number of cords which support the 
movable pulley blocks. 

Write simple descriptions of the work done in each 
part of the experiment, shortening the descriptions by 
references to the diagrams. 

Observations 





Pulleys used 


Weights of 


Balance Beading 


Trials 


Load 


Pan 


Movable 
Block 


Up 


Down 


1 and 2 

3 and 4 

5 and 6 

7 and 8 

9 and 10 

11 and 12 

13 and 14 

etc. 


1 fixed 

1 fixed 
1 movable 
1 movable 

1 fixed and 1 mov. 

2 fixed and 1 mov. 
2 fixed and 1 mov 

etc. 


100 g. 
200 g. 
100 g. 
200 g. 
200 g. 
200 g. 
500 g. 
etc. 











For Part (<?) only ; Trials 11 to 18 



Number of 


Eesistance 
(Total Load) 


Effort 

(Average Balance) 


Distance moved Through 


Trials 


Resistance 


Effort 


11 and 12 










13 and 14 










15 and 16 










17 and 18 











106 



LABORATORY EXERCISES 



Except in Part (a), the total load (resistance) is the 
sum of the weights on the pan, the weight of the pan, and 
the weights of the movable blocks used. The average of 
the two balance readings in each trial is the effort. The 
mechanical advantage of a machine is defined as the re- 
sistance divided by the effort. Record these calculated 
results in a table at the top of the right-hand page. 

Calculated Results 



Ti:i us 



I*ii UK TB 
DBHD 



E&B8I8TAN01 (K) 

(Total Load) 



Effort (E) 
I \ Forage 
Balances | 



Mr. ii wn ai. 
\ i>\ \ \ i L6B 

A' -- E 



Cords supporting 
Movable Block 



Discussion: 

Under this heading on the right-hand page (or the 
second right-hand page) answer the italicized questions 
occurring in the experimental directions. 

Conclusion: 

After comparing in each case the number representing 
the mechanical advantage with the number of cords sup- 
porting the movable block or blocks, answer the following 
question: 

How may the mechanical advantage of a set of pulleys 
be stated in terms of the machine's construction? 



THE WHEEL AND AXLE 107 

EXPERIMENT 29 

The Wheel and Axle 

OBJECT. To study the operation of the wheel and axle and to 
find its mechanical efficiency. 

Apparatus. Wheel and axle with several diameters ; metric 
weights (500 g. and 1000 g.) ; spring balance (2000 g.) in case 
apparatus has not an exact simple ratio ; fish line ; stand and 
clamp for wheel and axle in case it is not mounted on its own 
base ; pair of calipers (or a pencil compass) is convenient for 
measuring the radii ; meter stick. 

Introductory : 

The windlass is used to lift a bucket from a well or 
dirt from an excavation. Several men on a capstan can 
pull out of the water a heavy anchor which they could not 
lift with their hands from the deck of the vessel. The 
devices for accomplishing these rather difficult tasks are 
applications of the wheel and axle, one of the simple 
machines. In the illustrations just given, a lesser effort 
overcomes a larger resistance, or there is a mechanical ad- 
vantage greater than one. Upon, what does the mechani- 
cal advantage of a wheel and axle depend ? 

Experimental : 

One cord is attached to the axle and another cord to 
the wheel. On the axle cord is attached the load (resist- 
ance) ; on the wheel cord are attached weights which act 
as the effort and just balance the load. When the weights 
on the two cords are in equilibrium, the slightest pull on 
the cord in either direction should make the weights run 
freely up and down at a gentle rate. 

The weights may be attached by a slip noose in the 



108 



LABORATORY EXERCISES 



free end of the cord. The first load may be conveniently 

1000 grams. The distances traveled by the effort and 
the resistance in the same time are measured 
with a meter stick. The radius of the axle 
and the radius of the wheel are also deter- 

"^F^^liP m i ne( l- AH these measurements are to be 
recorded in tabular form near the top of 
the left-hand page. 

At the direction of the instructor, meas- 
urements with additional loads are made. 
In case there are several wheels on the axle, 
one of the smaller wheels may be taken for 
a new axle. For some. of the measurements 

it may prove necessary to use a spring balance in place 




Fig. 44. 



of the effort weight. 



( Observations 



Nl MliKR OF 

Trial 



1 

2 

etc. 



Load oh \w.\: 
(Resistance) 



1000 g. 

etc. 



El POBT OH 

Willi i. 



K LDIU8 OF 

A \I.K 



Radius of 
Wheel 



For Two Headings Only 



Number of 


Load 
(Resistance) 


Effort 


Distance Moved Through 


Trial 


Eesistance 


Effort 













Make a drawing of the wheel and axle used and write a 
simple description of how the experiment was done. 



THE WHEEL AND AXLE 



109 



The mechanical advantage of a simple machine like the 
wheel and axle, is the ratio of the resistance to the effort. 
Calculate this for each trial. Also find in each case the 
ratio of the radius of the wheel to the radius of the axle. 
Place all the calculated results in tabular form at the top 
of the right-hand page. 

Calculated Results 



Number of 
Teial 


Resistance (A j ) 
(Load) 


Effort (E) 


Meciianical 
Advantage B -$- E 


Radius Wheel 
Radius Axle 













Discussion : 

What is sacrificed in gaining the mechanical advantage 
of the wheel and axle ? 



Conclusion : 

Complete the following statement: The mechanical 
advantage of the wheel and axle may be stated in terms 

of its construction as the ratio of the 

to the — 



110 LABORATORY EXERCISES 

EXPERIMENT 30 

Mechanical Efficiency of Machines 

OBJECT. — To find the mechanical efficiency of an inclined plane, 
a set of pulleys, and a wheel and axle. 

Apparatus. As designated for the inclined plane (page 99), 
for the pulley (page 102), and for the wheel and axle (page 107). 

In the experiments on those machines, measurements were 
made and tabulated which will serve for this experiment. 

Commercial block and tackle with necessary weights in case 
Part (b) is to be done. 

Introductory : 

The rapid growth of the manufacturing 1 industries in 
the United States has been due in large part to the develop- 
ment of efficient machinery. To be efficient, a machine 
must return, in some form of useful output, a large part of 
the energy applied to it. Machines which waste too much 
of the applied energy in friction, in loss of motion, or in 
other ways, are condemned to the scrap heap when a 
more efficient machine for the same purpose is devised. 
Calculations of the efficiency of complicated machinery 
are difficult even for a competent mechanical engineer, 
but a student can learn from the inclined plane, the pulley, 
and the wheel and axle, the main factors in the efficiency 
of any machine. These factors are in accordance with 
the law of work, — " the amount of work put into a perfect 
machine equals the work gotten out of it." 

The mechanical efficiency of a machine is the percentage 
of total work done on the machine which proves useful. 

Experimental : 

(a) The instructor may direct the use of the readings 
obtained in the experiments on the inclined plane, the 



MECHANICAL EFFICIENCY OF MACHINES 111 

pulley, or the wheel and axle. In all cases, the effort 
readings used must be ones taken while the weight (re- 
sistance) is being raised, without correction for friction. 
These are the conditions under which a machine does use- 
ful work. 

The weight raised, the height of the plane, the force 
with load ascending, and the length of the plane are the 
readings to be taken from the inclined plane experiment. 

It should be noted with regard to the inclined plane 
that the load (resistance) moves through a useful distance 
equal to the height of the plane while the effort is moving 
the length of the plane. The effort is the force used with 
the load ascending. 

In the pulley and the wheel and axle experiments, most 
of the readings necessary for this experiment were tabulated 
in the second table of observations. The effort reading to 
be taken from the pulley experiment is not the " average 
balance," but the balance reading with the load ascending, 
recorded in the first table of observations. 

The observations taken from previous experiments 
should be again tabulated near the top of the left-hand 
page used for this experiment. Any new observations 
made at the direction of the instructor may be tabulated 
in the same form. 

(5) During the laboratory hour, if the instructor so 
directs, a test will be made on the efficiency of a commer- 
cial block and tackle with as large a load as is safe and 
desirable. The students designated by the instructor to 
make the test will report the results to the class. Com- 
parison can then be made between the school apparatus, 
designed to show the law of work, and commercial appa- 
ratus, made to stand the wear and tear of actual service. 

In a perfect machine, the amount of work obtained 
from it equals the amount of work put into it, i.e. resist- 



112 



LABORATORY EXERCISES 



ance x resistance distance = effort x effort distance. 
Calculate these two products for each observation. 

Then calculate the mechanical efficiency of each machine 
from the two products, recalling that 

useful work (work output) 



Efficiency = 



total work (work input) 



Observations 



Machine 


Kf.si-.-i ance 
(Load or Weight lifted) 


Effort 

(Force applied) 


Distance moved THROUGH 


Resistance 


Effort 













At the top of the right-hand page tabulate the results 
of all calculations. 



Calculated Results 



Machine 



Obi i ci, Work 
(Resistance X 

Resistance Distance) 



Total Work 
(Effort X 

Effort Distance) 



Mecii. Efficency 
/ Useful Work \ 
V Total Work/ 



Discussion : 

What may make the mechanical efficiency vary in dif- 
ferent observations of the same machine? 

Conclusion : 

The average mechanical efficiency found from my ob- 
servations was for the inclined plane %, for the 

pulleys %, and for the wheel and axle %. 

(state combination used) 



COEFFICIENT OF FRICTION 113 

EXPERIMENT 31 

Coefficient of Friction 

OBJECT. To determine the ratio of the friction between two 
surfaces to the pressure holding them together. 

Apparatus. Rectangular wooden block ; board with uniform 
surface, with support for use as inclined plane ; spring balance 
(2000 g.) ; fish line ; block of weights ; meter stick. 

Introductory : 

Heavy loads on a wagon press down and increase the 
friction at the axles. The ratio between the friction and 
the pressure causing it, is called the coefficient of friction. 

This fraction has different values according to the 
kinds of surface in contact. For instance, there is more 
friction between rubber soles and a polished floor than 
between leather soles and the same floor. The man with 
the rubber soles can walk up a steeper plank, but even he 
will begin to slip when the pitch of the plank is increased 
to a certain definite angle. The leather soles slip at 
a smaller definite angle of pitch. 

The coefficient of friction may be found, either by 
measuring both friction and pressure directly, or by find- 
ing the angle of elevation of the surface of one body, at 
which the weight of a second body will just cause the 
latter to slip down the inclined surface of the first. 

Experimental : 

(#) A hard wood block, with various weights upon it, 
is dragged over the surface of a smooth horizontal board 
by means of a cord attached to the block and to a spring 
balance* If the block is kept moving at a uniform speed, 



114 



LABORATORY EXERCISES 



the reading of the balance will show the amount of the 
friction between the surfaces. The pressure between the 



IX> 




-c- 



Fig. 45. 

surfaces is the weight of the block plus the load placed 
upon it. Several weights ranging from 100 to 1000 grams 
should be used to load the block. From these readings 
the coefficient of friction may be found by dividing the 
friction by the pressure causing it. 

(6) Using the same block and board, with a support to 
adjust the board to any desired inclination, the board m*iy 

/ V 



A 














Fig. 46. 

be raised gradually until the unloaded block will just 
slide down with uniform motion if the board is constantly 
tapped with the finger. This angle is called the limiting 



COEFFICIENT OF FRICTION 



115 




Fig. 47. 



angle of friction. Referring to Fig. 46, AC and BO should 
be measured. 

When a body rests on an inclined plane, its weight, w, 
is resolved into two component forces. One of these, jt>, is 
perpendicular to the plane and 
produces pressure upon it. 
The other component / acts par- 
allel to the plane and toward the 
lower end. As this is the only 
component of the force that acts 
in the direction in which the 
body on the plane may move, it 
is evident that only this force needs to be balanced to 
keep the body from moving down the plane. Therefore, 
at the limiting angle, the component / of the weight w, 
as it urges the block down the plane, just balances the 
friction. 

It will be readily seen (Fig. 47) that the triangles fwp f 

f BC f 

and ABC are similar. Hence, J --= — — . But - is the 

p AC p 

friction divided by the pressure and is, therefore, the 
quantity we seek. Its value, then, may be calculated by 
dividing the height of the plane by the length of the base. 
Record the readings in tabular form near the top of the 
left-hand page. 



Observations 

Part (a) : 

i 

Total pressure (block and weight) g. 

Beading of balance . . . . g. 

Part (b) : 

Height of plane 

Length of base . 



Etc; 

9- ff- 

ff- 9- 



cm. 
cm. 



116 LABORATORY EXERCISES 

Make a clear outline drawing of your apparatus and 
briefly describe your work in both (a) and (6). 

Place the calculated results in tabular form at the top 
of the right-hand page. 



Part (a) 



Calculated Results 



Coefficient of friction (J- — ) 



\pressurej 



.pressure. 

Etc. Average 



Part (J) 



Coefficient of friction ( - ■& - 

\ base 



Discussion : 

Is the coefficient of friction dependent upon the load? 
Show why the ratio of the height to the base of the in- 
clined plane at the limiting angle is equal to the coefficient 
of friction. 

Conclusion : 

The coefficient of friction between and is 

(name materials) 



EXPERIMENT 32 

Vibrations of a Tuning Fork 

OBJECT. To determine the frequency of a given tuning fork. 

Apparatus. A low frequency tuning fork (not over 1 28 V.P.S.) 
with considerable amplitude of vibration, preferably made of bell 
metal, and with a bristle or stylus attached ; oval piece of wood ; 
glass plate smoked ; pendulum beating known fraction of a second, 
provided with a stylus ; rigid clamps for tuning fork and pendu- 



VIBRATIONS OF A TUNING FORK 117 

lum ; holder and track for glass plate ; candle, or cake of " Bon 
Ami." 

Note. — Apparatus dealers furnish sets of the above ap- 
paratus. 

Introductory : 

A knowledge of the number of vibrations correspond- 
ing to each musical note is essential to the understanding 
of the Physics of Sound. While the ear may be trained 
to estimate very closely the pitch of the tuning fork, the 
eye is not quick enough to count its vibrations. By pro- 
viding the fork with a tracing point and by drawing pre- 
pared glass or paper under the fork at right angles to the 
direction in which the fork is vibrating, each complete back 
and forth vibration of the fork will be represented by a 
wave-shaped mark. If a pendulum provided with a trac- 
ing point is so placed that it also vibrates across the glass, 
the distance the glass moved during the known period of 
the pendulum is also recorded. Then the number of vi- 
brations of the tuning fork in that period may be counted. 

Experimental : 

The best way of preparing the glass is to rub over it a 
thin coat of "Bon Ami" or of whiting and alcohol, and 
allow it to dry. The apparatus should then be carefully 
inspected and adjusted so that the tracing points of both 
the fork and the pendulum will sweep across the plate in 
as nearly the same line as they can without interfering 
with each other. The tracing points must bear on the 
surface hard enough to scratch away the coating, but not 
with pressure enough to check the motion of either fork 
or pendulum. This may be tested by setting each in 
vibration with the glass at rest. 

The fork is best set vibrating by placing between the 



118 



LABORATORY EXERCISES 



prongs an oval stick of wood, thick enough to spread the 
prongs the desired amount, and then suddenly pulling it 
out. 

When all adjustments are made, set pendulum and 
tuning fork in vibration and with a steady, even motion 
draw the glass along the track at such a rate as to have 




Fig. 48. A Vibrograph. 



at least one complete swing of the pendulum, back and 
forth, recorded on the glass. Remove the glass, to permit 
others to use the apparatus. 

The number of complete wave forms traced by the fork 
between two successive points where the pendulum wave 
crosses the tuning fork wave, is the number of vibrations 
made by the tuning fork in the period of the pendulum. 

Place in tabular form, near the top of the left-hand page, 
the time of the pendulum period and the number of vibra- 
tions recorded each time during that period. 



Observations 



Trial 

Observed vibrations 
Period of pendulum 
Number of fork . 



VIBRATIONS OF A TUNING FORK 119 

Make a simple drawing of your apparatus and describe 
briefly the essentials of the method. 

Calculate the average number of vibrations for the 
period of the pendulum, and from the average find the 
number of vibrations per second. Record the calculated 
results at the top of the right-hand page. 

Calculated Results 

Average number of vibrations in sec. was . . 

Frequency of fork (vibrations per second^ . . . 



Discussion : 

(a) Explain fully why a complete wave trace of the 
fork stands for one vibration of the fork. 

(6) Why does a half wave trace stand for the period 
of the pendulum ? 

Conclusion : 

The frequency of fork No. is vibrations per 

second. 



120 LABORATORY EXERCISES 

EXPERIMENT 33 

The Velocity of Sound in Air 

OBJECT. To determine the approximate velocity of sound in the 
open air at the existing conditions. 

Apparatus. Pendulum (J sec.) with large-faced bob 1 and 
mounted in a shallow box ; pair of field glasses ; measuring tape ; 
two short pieces of board ; thermometer. 

Introductory : 

A flash of lightning is usually seen before the thunder, 
the sound accompanying the electric discharge, is heard. 
The steam escaping from the whistle on a distant loco- 
motive may be noticed several seconds before the sound 
reaches our ears. The Hash of a gun is evident before 
the sound of the discharge is heard. All these illustra- 
tions show that sound travels much more slowly than 
light, and that an appreciable interval is required for a 
sound to travel any considerable distance. Since light 
has such great velocity, the time required for it to travel a 
part of a mile is not measurable by any ordinary means, 
while the comparatively slow-traveling sound takes a 
noticeable time for the same distance. These relative 
velocities make possible a simple method for determining 
the number of feet per second traveled by a sound. 

Experimental : 

Mount the pendulum beating three fourths of a second 
in a shallow wooden box with the cover removed. Stretch 

1 In case a pendulum with a brass bob is not available, a pendulum 
may be made with a 5-lb. slotted weight and a wooden bar, or a good bob 
could be cast of lead with a small brass curtain rod inserted, in the cover 
of a coffee tin or lard pail. Whatever large-faced bob is used, one face 
should be painted a blue similar to that used in the enameled street signs. 



THE VELOCITY OF SOUND IN AIR 121 

across the box opening an opaque white cloth and in it 
make a hole the shape and size of the pendulum bob at 
the center of its vibration. At the back of the hole and 
on the bottom of the box arrange a white background. 
The exposed face of the bob should be painted blue, since 
this color will be readily seen as the bob swings across 
the opening. 

Set the pendulum about 500 feet away, so placed that the 
bob of the pendulum is several feet from the ground. One 
student is stationed at the box with two short boards and 
strikes them together so as to produce a sharp sound every 
time the bob is at the center of its swing. 

Observers should move either toward or away from the 
pendulum until a position is obtained where the successive 
sounds produced coincide with the successive swings of 
the bob across the opening. This means that the sound 
produced at the center of one beat of the pendulum 
reaches the observer at the center of the next beat. Then 
during the time of one beat, the sound travels the distance 
of the pendulum from the observer. Field glasses will be 
necessary to see clearly the swing of the bob across the 
opening. 

Make one determination with the wind, and one against 
it, and record the distances as measured with a tape. 

Take the temperature of the air and record in the table 
of observations. 

Observations 

Distance of observer to pendulum, with wind , ft. 

Distance of observer to pendulum, against wind ft. 

Temperature of air °(7. 

Make drawings showing how the pendulum was set up 
and describe the method of the experiment. 



122 LABORATORY EXERCISES 

Calculated Results 

Average distance traveled by sound in | second ft. 

Velocity of sound per second ft. 

Conclusion : 

The velocity of sound per second in the open air at °C. 

was _ 



EXPERIMENT 34 

Sympathetic Vibrations 

OBJECT. To set a tuning fork into vibration by sympathetic 
vibrations with another fork of the same frequency. 

Apparatus. Two tuning forks of the same frequency, 1 as 
256 V.P.S. ; tuning fork of different frequency, as 384 V.P.S. ; 
flat cork about 2" in diameter; 500-gram weight or iron ball 
with fish line for suspension ; support for hanging weight. 

Introductory : 

When the loud pedal of a piano is pressed, dampers are 
lifted from the strings so that the strings can vibrate 
freely. Then a note sung into the piano will make one 
wire vibrate in response, so that a note of the same pitch 
can be heard. The sound vibrations produced by the 
human voice have been the stimulus to the production 
of a sound by the vibration of one of the piano wires. 

1 Xote to Instructor. — Two forks stamped with the same frequency 
number will rarely vibrate at the same rate without filing notches in the 
end of one of them. Do this by taking two forks that sound nearly alike 
and than raise the pitch of the lower (flat) fork by filing the outer end 
of one prong. Then stamp or file an identifying number on the handle 
of both forks. Always give out together that pair of forks for this 
experiment. 



SYMPATHETIC VIBRATIONS 123 

Since the stimulating sound and the sound produced have 
the same pitch (frequency of vibration), this is a case of 
sympathetic vibrations. Tuning forks are very convenient 
instruments for studying sympathetic vibrations, for their 
rate of vibration per second is known. Usually the fre- 
quency number is stamped at the base of the two prongs. 

Experimental : 

(a) Suspend a 500-gram weight (or a ball of about the 
same weight) by a light, strong cord about a meter in 
length. 

When the weight is at rest, give it a light tap with a 
lead pencil, noting the direction in which the weight be- 
gins to move or vibrate. When the weight is at the 
center of its swing and moving from you, tap again. Con- 
tinue in this manner until the weight has received about 
twenty gentle taps. What is the effect upon the vibra- 
tions of the suspended weight ? From what source did 
the weight get its impulses ? 

With the weight again at rest, give it, without paying 
any attention to the intervals, twenty more gentle taps, 
hitting the weight just as it happens to be coming toward 
or going away from you. What is the effect on the vi- 
bration of the weight ? Compare the regularity in time 
of this second tapping with that of the first. What rela- 
tion existing between the regularity of the tapping and the 
vibration of the weight, caused such a marked effect in the 
first case ? 

(5) The following directions must be followed exactly 
in order to secure the desired result. Study them thor- 
oughly before beginning the experiment. Examine the 
forks to see that the same number is marked on the stem 
of each. 

(1) Hold the two forks by the stem, not allowing the 



124 LABORATORY EXERCISES 

fingers to touch any other part of the fork (in order to 
avoid heating). 

(2) Set the fork held in the right hand into vigorous 
vibration by striking the end of one of its prongs sharply 
against a cork on the desk. 

(3) Steady the fork in the left hand by allowing 
the hand to rest against the desk with the fork held 

horizontally. 



■ ^ j (4) Bring the vibrating 

/ ^- L i fork into a position paral- 

v i lei to the other fork, with 

Fig. 49. the prongs extending in 

an opposite direction and 
the two forks about ^ of an inch apart (Fig. 49). 

(5) After the forks have been in this position while 
you count three, slowly bring the left-hand fork near 
the ear and determine whether it has been set into 
vibration. 

(6) If the first trial has not been successful, repeat the 
work. 

Apply to the instructor for a tuning fork of different 
frequency from that of the two forks used. With this 
fork and one of the former ones repeat the experiment, 
noting the success of your efforts. 

Make a drawing showing the forks in the position 
where sympathetic resonance was obtained. Write a full 
description of the experiment and its results. 

Conclusion: 

Answer the italicized question in Part (a). What must 
be true of the frequencies of two forks in order that one 
of them may be set into sympathetic vibration by the other? 



LEFe 7 !3 



